A390519 a(n) = Sum_{k=0..n} (4*k+1) * binomial(3*n+k+1,n-k)/(3*n+k+1).

1, 2, 9, 47, 262, 1516, 8988, 54213, 331233, 2044151, 12716872, 79636493, 501466519, 3172569392, 20152910577, 128468322235, 821489663702, 5267495309068, 33859098223050, 218126618867172, 1408032403175424, 9105604254844341, 58983284099194233, 382660622126950875

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: g/(1 - x*g^4), where g = 1+x*g^3 is the g.f. of A001764.

G.f.: 1/(1 + 1/g - g), where g = 1+x*g^3 is the g.f. of A001764. - Seiichi Manyama, Dec 08 2025

Mathematica

Table[Sum[(4*k+1)*Binomial[3*n+k+1, n-k]/(3*n+k+1), {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 11 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (4*k+1)*binomial(3*n+k+1, n-k)/(3*n+k+1));
(Magma) [&+[(4*k+1)*Binomial(3*n+k+1, n-k)/(3*n+k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 11 2025

Crossrefs

Cf. A047098, A390520.

Cf. A001764.

Sequence in context: A002395 A356142 A042793 * A059272 A379434 A228341

Adjacent sequences: A390516 A390517 A390518 * A390520 A390521 A390522

Keyword

nonn

Author

Seiichi Manyama, Nov 08 2025

Status

approved