A371580 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x)^2 )^2.

1, 2, 15, 126, 1211, 12544, 136668, 1543696, 17914325, 212308682, 2558783193, 31265632206, 386430721728, 4822586987324, 60686262591525, 769167948066520, 9810280980482827, 125819903217235130, 1621648696092783746, 20993171222948561746, 272848383910348808089

Offset

0,2

Links

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

Formula

a(n) = 2 * Sum_{k=0..n} binomial(5*k+2,k) * binomial(2*k,n-k)/(5*k+2).

Prog

(PARI) a(n, r=2, s=2, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A371578, A371585.

Sequence in context: A364978 A396557 A051407 * A390743 A242091 A132182

Adjacent sequences: A371577 A371578 A371579 * A371581 A371582 A371583

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved