A371540 G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^5.

1, 5, 35, 310, 3055, 32151, 353755, 4019825, 46808750, 555621400, 6698027100, 81779512155, 1009194553315, 12567338972700, 157725047958100, 1992990741398625, 25333585976926275, 323725357496659565, 4156196637610760235, 53585106340408250725, 693491493195479127175

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349362, A371537, A371538, A371539, A371541.

Cf. A371494, A371495, A371496.

Cf. A371519.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+4,k)/(k+1).

G.f.: A(x) = B(x)^5 where B(x) is the g.f. of A349362.