A390811 a(n) = Sum_{k=0..n} (2*k+3) * binomial(4*n-2*k+3,n-k)/(4*n-2*k+3).

1, 4, 21, 129, 871, 6255, 46894, 362852, 2876277, 23238219, 190660664, 1584290757, 13305632458, 112764573331, 963162517251, 8282773672193, 71654165901031, 623158691439348, 5445003027343549, 47778125485389799, 420835005922449552, 3719562384259486624

Offset

0,2

Links

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

Formula

G.f.: g^3/(1-x*g^2) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[(2*k+3)*Binomial[4*n-2*k+3, n-k] / (4*n-2*k+3), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 28 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (2*k+3)*binomial(4*n-2*k+3, n-k)/(4*n-2*k+3));
(Magma) [&+[(2*k+3)*Binomial(4*n-2*k+3, n-k)/(4*n-2*k+3): k in [0..n]] : n in [0..40] ]; // Vincenzo Librandi, Nov 28 2025

Crossrefs

Cf. A002293, A390778, A390810.

Sequence in context: A300674 A371430 A232956 * A234268 A384270 A111177

Adjacent sequences: A390808 A390809 A390810 * A390812 A390813 A390814

Keyword

nonn

Author

Seiichi Manyama, Nov 20 2025

Status

approved