A378840 G.f. A(x) satisfies A(x) = ( 1 + x * A(x)^(4/3) * (1 + A(x)^(1/3)) )^3.

1, 6, 66, 902, 13794, 225990, 3878946, 68854278, 1253647938, 23283474310, 439394508162, 8401507608966, 162413310158626, 3169029168475206, 62330703549363810, 1234503404283308038, 24599422679682518658, 492824963618477891334, 9920626149798702401730

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = 3 * Sum_{k=0..n} binomial(n,k) * binomial(4*n+k+3,n)/(4*n+k+3).

Conjecture: g.f.: B(x)^3, where B(x) is the g.f. of A260332.

Prog

(PARI) a(n, r=3, t=4, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));

Crossrefs

Cf. A260332, A365847, A371676.

Cf. A006320, A033296, A365843.

Sequence in context: A130977 A191096 A151832 * A133306 A371681 A216636

Adjacent sequences: A378837 A378838 A378839 * A378841 A378842 A378843

Keyword

nonn

Author

Seiichi Manyama, Dec 09 2024

Status

approved