A371521 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^6.

1, 6, 57, 614, 7158, 88002, 1123689, 14760024, 198172050, 2707560544, 37522666803, 526190125308, 7452866846847, 106465245105972, 1532129408941797, 22191180837313808, 323243244688652943, 4732225866305323686, 69591395772704207770, 1027547992261749954798

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349333, A371379, A371519, A371522, A371523.

Cf. A045868, A371516, A371517, A371520.

Programs

PARI

a(n) = 6*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+5, k)/(5*k+6));

Formula

a(n) = 6 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+5,k)/(5*k+6) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+6,k)/(k+1).

G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A349333.