A378462 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(2*n+k-1,n-2*k).

1, 1, 5, 28, 157, 891, 5126, 29814, 174869, 1032481, 6128795, 36541220, 218672950, 1312712519, 7901609196, 47673716238, 288226881669, 1745734656930, 10590673033931, 64342403492274, 391414638274987, 2383907483199039, 14534764399148966, 88705912126094358

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = [x^n] 1/(1 - x - x^2/(1 - x)^2)^n.

Prog

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

Crossrefs

Cf. A002002, A213684.

Cf. A378467.

Sequence in context: A271808 A005785 A027912 * A243669 A327999 A254538

Adjacent sequences: A378459 A378460 A378461 * A378463 A378464 A378465

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2024

Status

approved