A395708 Expansion of g^4*(4*g-3)/(3-2*g)^4, where g = 1+x*g^3 is the g.f. of A001764.

1, 16, 174, 1632, 14155, 116976, 935466, 7305600, 56039319, 423871680, 3170138664, 23491004544, 172729245780, 1261775774896, 9165443521170, 66252625110528, 476863764588543, 3419357185775376, 24436269617844174, 174107947439614560, 1237159520885096739

Offset

0,2

Links

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

Formula

a(n) = (n+1) * A062236(n+1).

G.f.: (Sum_{k>=0} (6*k+1)/(3*k+1) * binomial(3*k+1,k) * x^k) * (Sum_{k>=0} binomial(3*k,k) * x^k)^3.

Sum_{k>=1} a(k-1) * x^k/k^2 = (1/2) * log( Sum_{k>=0} binomial(3*k-1,k) * x^k ).

a(n) = (n+1) * Sum_{k=0..n} binomial(3*k+2+l,k) * binomial(3*n-3*k-l,n-k) for every real number l.

a(n) = (n+1) * Sum_{k=0..n} 2^(n-k) * binomial(3*n+3,k).

a(n) = (n+1) * Sum_{k=0..n} 3^(n-k) * binomial(2*n+k+2,k).

Prog

(PARI) a(n) = (n+1)*sum(k=0, n, 2^(n-k)*binomial(3*n+3, k));

Crossrefs

Cf. A033504, A395709, A395710, A395711.

Cf. A001764, A062236.

Sequence in context: A021374 A253343 A215687 * A187720 A017931 A387340

Adjacent sequences: A395705 A395706 A395707 * A395709 A395710 A395711

Keyword

nonn

Author

Seiichi Manyama, May 04 2026

Status

approved