A390810 a(n) = Sum_{k=0..n} (k+3) * binomial(4*n-3*k+3,n-k)/(4*n-3*k+3).

1, 4, 20, 119, 789, 5605, 41729, 321343, 2538402, 20454598, 167477778, 1389362192, 11652787785, 98645677902, 841765475559, 7232902254592, 62527470065085, 543449477933689, 4745931534721033, 41623798439531180, 366467937251944756, 3237773143564597657

Offset

0,2

Links

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

Formula

G.f.: g^3/(1-x*g) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[(k+3)*Binomial[4*n-3*k+3, n-k] / (4*n-3*k+3), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 28 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+3)*binomial(4*n-3*k+3, n-k)/(4*n-3*k+3));
(Magma) [&+[(k+3)*Binomial(4*n-3*k+3, n-k)/(4*n-3*k+3): k in [0..n]] : n in [0..40] ]; // Vincenzo Librandi, Nov 28 2025

Crossrefs

Cf. A002293, A390778, A390811.

Sequence in context: A258666 A391199 A128236 * A091046 A101055 A208232

Adjacent sequences: A390807 A390808 A390809 * A390811 A390812 A390813

Keyword

nonn

Author

Seiichi Manyama, Nov 20 2025

Status

approved