A364924 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - 2*x*A(x)^4).

1, 1, 7, 67, 743, 8970, 114445, 1517976, 20722023, 289224355, 4108588558, 59207805442, 863439906413, 12718638581368, 188960182480440, 2828238875318256, 42605850936335463, 645497106959662857, 9829072480785776101, 150345303724987825021

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} 3^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} 3^(n-k) * binomial(n,k) * binomial(4*n,k-1) for n > 0.

Prog

(PARI) a(n) = sum(k=0, n, 3^k*(-2)^(n-k)*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));

Crossrefs

Cf. A007564, A364923.

Cf. A243667.

Sequence in context: A038386 A371398 A243675 * A082578 A291814 A253386

Adjacent sequences: A364921 A364922 A364923 * A364925 A364926 A364927

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2023

Status

approved