A371433 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x) ).

1, 2, 5, 11, 11, -77, -704, -3795, -15686, -48598, -74009, 376623, 4438840, 27458060, 126898948, 440550682, 849522927, -2621906045, -39993434701, -270428078305, -1339005344985, -5014789377825, -11407684195950, 18849058485855, 417417757017612, 3058172078113944

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A371434, A371435.

Cf. A369215.

Sequence in context: A091114 A155767 A079782 * A093554 A168453 A136990

Adjacent sequences: A371430 A371431 A371432 * A371434 A371435 A371436

Keyword

sign

Author

Seiichi Manyama, Mar 23 2024

Status

approved