PASS the two brute forces agree for n <= 11 (counts, sum- and skew-indecomposable)  [allperms n<=11, enum_prepend n<=16]
PASS J_n = 1 for n = 1 and n-1 for n >= 2 (Lemma 3.3)
PASS specification (S1)-(S3) has integer coefficients to order 40
PASS f, E, I from (S1)-(S3) equal the brute-force counts |C_n|, sum-indec., skew-indec. for 1 <= n <= 16
    f  = [1, 1, 2, 6, 21, 77, 290, 1118, 4398, 17595, 71385, 293042, 1215035, 5081259, 21408350, 90786332, 387212538, 1659936246, 7148446212, 30910820373]
    E  = [0, 1, 1, 3, 10, 34, 120, 440, 1665, 6460, 25570, 102868, 419418, 1729346, 7198540, 30209860, 127680421, 542985538, 2321800695, 9976338356]
    I  = [0, 1, 1, 3, 11, 43, 170, 678, 2733, 11135, 45815, 190174, 795617, 3351913, 14209810, 60576472, 259532117, 1116950708, 4826645517, 20934482017]
PASS (S1) f = 1/(1-E) on the brute-force series mod z^17
PASS (S2) I = z + E^2/(1-E) on the brute-force series mod z^17
PASS (S3) E = z + J I/(1-J) on the brute-force series mod z^17
PASS Q^2 - 4PR = D = 1-8z+20z^2-24z^3+16z^4-4z^5
PASS Q^2 = 1-4z+8z^2-8z^3+4z^4 and 4PR = 4z-12z^2+16z^3-12z^4+4z^5 (as printed)
PASS P f^2 - Q f + R = 0 on the series mod z^41 (equation (1))
PASS (1-z)^2 E^2 - (1-2z) E + z(1-z)^2 = 0 on the series (equation (3))
PASS (Q - 2Pf)^2 = D on the series (equation (4))
PASS Q - 2Pf equals the power series sqrt(D) with constant term 1
    sqrt(D) = ['1', '-4', '2', '-4', '-10', '-34', '-124', '-468', '-1810', '-7140', '-28630', '-116376']
PASS numerator Q - sqrt(D) has zero constant term
PASS closed form (2) re-expands to f (mod z^40)
PASS Theorem 1.1(b): f = 1+z+2z^2+6z^3+21z^4+77z^5+290z^6+1118z^7+4398z^8+17595z^9+...
PASS Table 1 rows (n = 1..10) equal the series and the brute force
PASS Table 1 caption: |C_n| for n = 11..15 equal the series and the brute force
    |C_16| (series) = 387212538  brute force: 387212538
PASS sympy: eliminating I from (S2),(S3) gives a nonzero multiple of (3)  [factor -1]
PASS sympy: E = 1 - 1/f in (3), times f^2, gives (1)
PASS sympy: 1 + z - J = (1-2z)/(1-z)^2
PASS Remark 3.5: (1-x)^2 times the CMS equation is -(P F^2 - Q F + R)
PASS Remark 3.5: x(1-x)^2 + x^2 = P and P + (1-x)^3 = Q
PASS CMS Theorem 11 formula expands to f to order 15

24 checks, 0 failed
ALL CHECKS PASSED
