A395783 Expansion of (Sum_{k>=0} binomial(3*k+2,k) * x^k)^3.

1, 15, 159, 1460, 12405, 100449, 787390, 6030240, 45386460, 337036980, 2476230876, 18036064140, 130431953357, 937603882245, 6705639192060, 47748355535600, 338708562711465, 2394692570004255, 16881072760978035, 118691594469460080, 832588258306289580, 5828191882336453020

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{i,j,k >= 0 and i+j+k=n} binomial(3*i+2,i) * binomial(3*j+2,j) * binomial(3*k+2,k).

G.f.: (B(x)/x)^3 where B(x) is the g.f. of A025174.

a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(3*n+8,n-k).

a(n) = Sum_{k=0..n} (k+1) * 3^k * binomial(3*n+6-k,n-k).

a(0) = 1; a(n) = (1/n) * Sum_{k=0..n-1} (3*k+15) * 2^k * binomial(k+2,2) * binomial(3*n+8,n-1-k).

a(0) = 1; a(n) = (1/n) * Sum_{k=0..n-1} (2*k+15) * 3^k * binomial(k+2,2) * binomial(3*n+5-k,n-1-k).

Prog

(PARI) a(n) = sum(k=0, n, (k+1)*2^k*binomial(3*n+8, n-k));

Crossrefs

Cf. A025174, A386617, A395785.

Cf. A378483, A395779.

Sequence in context: A232414 A183555 A232415 * A016297 A206811 A027544

Adjacent sequences: A395780 A395781 A395782 * A395784 A395785 A395786

Keyword

nonn,easy

Author

Seiichi Manyama, May 05 2026

Status

approved