A371435 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x^4) ).

1, 3, 15, 91, 611, 4368, 32590, 250821, 1976441, 15865465, 129275835, 1066438399, 8888818659, 74743312480, 633272709348, 5400983817990, 46330852036920, 399479717666693, 3460229824525809, 30095179524446946, 262722158090170570, 2301201197665717770

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+2,n-4*k).

Prog

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

Crossrefs

Cf. A369124, A371432.

Cf. A369161.

Sequence in context: A047019 A099251 A364740 * A366090 A171790 A006632

Adjacent sequences: A371432 A371433 A371434 * A371436 A371437 A371438

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2024

Status

approved