A370837 Expansion of (1/x) * Series_Reversion( x/(x+1/(1+x^3)) ).

1, 1, 1, 0, -3, -9, -15, -6, 57, 231, 501, 474, -1223, -7331, -19655, -27813, 19089, 248541, 819141, 1508316, 417165, -8314449, -34737603, -78646452, -71651147, 251348311, 1461221581, 3984339966, 5586567405, -5424531663, -59608307151, -196443394947

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A370836, A370838.

Cf. A226974, A370800.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1+x^3)))/x)

PARI

a(n) = sum(k=0, n\3, (-1)^k*binomial(n, 3*k)*binomial(4*k, k)/(3*k+1));

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n,3*k) * binomial(4*k,k)/(3*k+1).