A371575 G.f. satisfies A(x) = ( 1 + x*A(x)^3 * (1 + x*A(x)) )^2.

1, 2, 15, 144, 1587, 18942, 238301, 3111788, 41779164, 573127760, 7998164674, 113189243386, 1620583793262, 23431706243230, 341654376602948, 5017986762425680, 74170837061591036, 1102479579201183898, 16469074050937364044, 247115476148847822586

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(s*k,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(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A000108, A143927, A365153, A368961, A371574.

Sequence in context: A371523 A219868 A224885 * A253571 A111686 A371582

Adjacent sequences: A371572 A371573 A371574 * A371576 A371577 A371578

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2024

Status

approved