A370799 Expansion of (1/x) * Series_Reversion( x/(x+1/(1-x+x^2)) ).

1, 2, 4, 7, 7, -18, -152, -648, -2076, -5006, -6442, 17866, 178102, 851516, 3004912, 7956103, 11925503, -24636636, -298702394, -1532903353, -5722053149, -16080843014, -27090920172, 37370086052, 584086176148, 3182365757908, 12407797520932, 36551266481968

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for reversions of series

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * b(k), where g.f. B(x) = Sum_{k>=0} b(k)*x^k satisfies B(x) = (1/x) * Series_Reversion( x*(1-x+x^2) ).

a(n) = (1/(n+1)) * Sum_{j=0..floor(n/4)} Sum_{k=0..floor((n-4*j)/3)} C(n+1,j)*C(n+k,k)*C(n+1-j,3*j+3*k+1)*(-1)^k*2^(n-4*j-3*k). - Tani Akinari, Dec 31 2025

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1-x+x^2)))/x)
(PARI) a(n)=(1/(n+1))*sum(j=0, n\4, sum(k=0, (n-4*j)\3, binomial(n+1, j)*binomial(n+k, k)*binomial(n+1-j, 3*j+3*k+1)*(-1)^k*2^(n-4*j-3*k))) \\ Tani Akinari, Dec 31 2025

Crossrefs

Cf. A370800, A370801.

Cf. A218225.

Sequence in context: A291810 A178183 A010759 * A063034 A351745 A094541

Adjacent sequences: A370796 A370797 A370798 * A370800 A370801 A370802

Keyword

sign

Author

Seiichi Manyama, Mar 02 2024

Status

approved