A390384 - OEIS

A390384

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

1, 6, 52, 518, 5480, 59883, 667788, 7551472, 86268736, 993247305, 11506149009, 133956128894, 1565956239176, 18369435931103, 216117213446306, 2549084979617775, 30132752342280996, 356891926172012205, 4234302321795870255, 50314550016599999131, 598692305693300128869

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OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

FORMULA

G.f.: 1/((1-5*x*g^4) * (1-x*g)) where g = 1+x*g^5 is the g.f. of A002294.

a(n) ~ 5^(5*n + 9/2) / (561 * sqrt(Pi*n) * 2^(8*n + 3/2)). - Vaclav Kotesovec, Nov 04 2025

MATHEMATICA

Table[Sum[Binomial[n+4*k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, binomial(n+4*k, k));