A388534 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k,k).

1, 5, 39, 347, 3263, 31635, 312735, 3133723, 31715191, 323436371, 3318437029, 34214183085, 354192729971, 3679209134983, 38329474641301, 400314931061877, 4190072084577255, 43941764631661091, 461609575980468465, 4856616177961798677, 51166644929473049733

Offset

0,2

Comments

Binomial transform of A388530.

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A388530(k).

a(n) = [x^n] ((1+x)^4 + x + x^2)^n.

Mathematica

Table[Sum[ Binomial[ n, k]*Binomial[n+3*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+3*k, k));
(Magma) [&+[Binomial(n, k)*Binomial(n+3*k, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 19 2025

Crossrefs

Cf. A001850, A388533, A388535, A388536.

Cf. A388530.

Sequence in context: A328554 A213233 A115187 * A378919 A266456 A365765

Adjacent sequences: A388531 A388532 A388533 * A388535 A388536 A388537

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2025

Status

approved