A371544 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^5.

1, 5, 30, 220, 1775, 15206, 135745, 1248900, 11758240, 112736305, 1096960024, 10804727805, 107520029780, 1079346767060, 10917110317185, 111149886462926, 1138205538056395, 11715403351807780, 121137702435412040, 1257720947476195045, 13106870738511517659

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

G.f.: A(x) = B(x)^5 where B(x) is the g.f. of A349361.

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(5*k+5, k)/(k+1));

Crossrefs

Cf. A349361, A371496.

Cf. A371520.

Sequence in context: A260351 A058247 A137965 * A129695 A110521 A318920

Adjacent sequences: A371541 A371542 A371543 * A371545 A371546 A371547

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved