A364865 G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^4).

1, 1, 3, 11, 43, 170, 657, 2392, 7675, 17603, -11898, -529678, -4783303, -33099464, -201744488, -1130700432, -5917753701, -28985131575, -131668554663, -540199800203, -1862208441834, -4014999475540, 10784817197302, 222255824910088, 1973412557775753

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

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

a(n) = (1/n) * Sum_{k=0..n-1} (-2)^k * binomial(n,k) * binomial(5*n-k,n-1-k) for n > 0.

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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));

Crossrefs

Cf. A291534, A364864, A364866.

Cf. A002294, A336540.

Sequence in context: A246758 A342632 A084643 * A302705 A007583 A356281

Adjacent sequences: A364862 A364863 A364864 * A364866 A364867 A364868

Keyword

sign

Author

Seiichi Manyama, Aug 11 2023

Status

approved