A388535 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+4*k,k).

1, 6, 58, 642, 7514, 90681, 1115926, 13919940, 175374298, 2226443808, 28436903193, 364990705338, 4703736180278, 60825549613913, 788847628263536, 10256308531408287, 133641112903039642, 1744719449385402828, 22816688728569237160, 298841865271667230260, 3919444959678438399769

Offset

0,2

Comments

Binomial transform of A388531.

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A388531(k).

a(n) = [x^n] ((1+x)^5 + x + x^2)^n.

Mathematica

Table[Sum[Binomial[n, k]*Binomial[n+4*k, k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Sep 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+4*k, k));
(Magma) [&+[Binomial(n, k)*Binomial(n+4*k, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 19 2025

Crossrefs

Cf. A001850, A388533, A388534, A388536.

Cf. A388531.

Sequence in context: A354228 A073848 A386919 * A141382 A212426 A259612

Adjacent sequences: A388532 A388533 A388534 * A388536 A388537 A388538

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2025

Status

approved