A371520 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^5.

1, 5, 40, 360, 3495, 35726, 378965, 4133080, 46059020, 522196465, 6004261226, 69849651025, 820651943130, 9723556336780, 116056250171385, 1394082307995626, 16840510019954835, 204453614350921540, 2493311080293185200, 30528431677508637205, 375155454309681439001

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A045868, A371516, A371517, A371521.

Cf. A349332, A371486.

Programs

PARI

a(n) = 5*sum(k=0, n, binomial(n-1, n-k)*binomial(5*k+4, k)/(4*k+5));

Formula

a(n) = 5 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(5*k+4,k)/(4*k+5) = Sum_{k=0..n} 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 A349332.