A371582 G.f. satisfies A(x) = ( 1 + x*A(x)^3 / (1 - x*A(x)) )^2.

1, 2, 15, 146, 1623, 19526, 247516, 3256118, 44037023, 608484766, 8552832116, 121908218724, 1757915510695, 25598937436696, 375916184707142, 5560517754432772, 82774606577536376, 1239110145377709862, 18641533742708676711, 281697878640036748684

Offset

0,2

Links

Table of n, a(n) for n=0..19.

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=1, t=6, 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. A006013, A211789, A365146, A371581.

Cf. A371575.

Sequence in context: A371575 A253571 A111686 * A001854 A060226 A325060

Adjacent sequences: A371579 A371580 A371581 * A371583 A371584 A371585

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved