A388536 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+5*k,k).

1, 7, 81, 1075, 15085, 218257, 3219975, 48151803, 727268605, 11068568815, 169477048531, 2607701303841, 40287043061611, 624531114465187, 9709707390848735, 151338206412401575, 2363968469638134445, 36997379456125484451, 580018004977692958353, 9106962882090829179795

Offset

0,2

Comments

Binomial transform of A388537.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A388537(k).

a(n) = [x^n] ((1+x)^6 + x + x^2)^n.

Mathematica

Table[Sum[ Binomial[ n, k]*Binomial[n+5*k, k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Sep 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+5*k, k));
(Magma) [&+[Binomial(n, k)*Binomial(n+5*k, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 19 2025

Crossrefs

Cf. A001850, A388533, A388534, A388535.

Cf. A388537.

Sequence in context: A088735 A364322 A339710 * A112119 A369024 A379856

Adjacent sequences: A388533 A388534 A388535 * A388537 A388538 A388539

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2025

Status

approved