A395735 Expansion of (Sum_{k>=0} binomial(5*k,k) * x^k)^4.

1, 20, 330, 5020, 72955, 1029420, 14227600, 193635980, 2604170265, 34691889640, 458581416780, 6022789170900, 78668860592525, 1022751344748320, 13242477343206240, 170851800208298220, 2197361112206094725, 28181571347810442300, 360526760664147197350, 4601781890365945572280

Offset

0,2

Links

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

Formula

a(n) = Sum_{i,j,k,l >= 0 and i+j+k+l=n} binomial(5*i,i) * binomial(5*j,j) * binomial(5*k,k) * binomial(5*l,l).

G.f.: B(x)^4 where B(x) is the g.f. of A001449.

a(n) = Sum_{k=0..n} 4^k * binomial(k+2,2) * binomial(5*n+3,n-k).

a(n) = Sum_{k=0..n} 5^k * binomial(k+2,2) * binomial(5*n-k,n-k).

a(0) = 1; a(n) = (20/n) * Sum_{k=0..n-1} 4^k * binomial(k+4,4) * binomial(5*n+3,n-1-k).

a(0) = 1; a(n) = (20/n) * Sum_{k=0..n-1} 5^k * binomial(k+4,4) * binomial(5*n-2-k,n-1-k).

Prog

(PARI) a(n) = sum(k=0, n, 4^k*binomial(k+2, 2)*binomial(5*n+3, n-k));

Crossrefs

Cf. A001449, A079678, A394916, A395660, A395736.

Cf. A378484, A378504.

Sequence in context: A304723 A273590 A187512 * A144507 A084032 A166984

Adjacent sequences: A395732 A395733 A395734 * A395736 A395737 A395738

Keyword

nonn,easy

Author

Seiichi Manyama, May 05 2026

Status

approved