A371584 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x))^2 )^2.

1, 2, 15, 138, 1435, 16074, 189238, 2308640, 28927579, 370084760, 4814147248, 63482437724, 846678807008, 11401357736202, 154800183842738, 2116833422071448, 29128279396373599, 403029526567463278, 5603854904038673961, 78260199678455985082, 1097257906416031628336

Offset

0,2

Links

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=2, s=2, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A371579.

Sequence in context: A347993 A215922 A285449 * A288950 A005415 A371523

Adjacent sequences: A371581 A371582 A371583 * A371585 A371586 A371587

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved