A390776 a(n) = (1/(2*n+1)) * Sum_{k=0..n} (2*k+1) * binomial(4*n+2,n-k).

1, 3, 16, 102, 712, 5255, 40288, 317548, 2556376, 20926236, 173634752, 1456967358, 12341344216, 105384541314, 906188676224, 7839788763224, 68189882357624, 595942751236292, 5230451316862912, 46082719298571192, 407420110891009312, 3613393386648632407, 32139376493886014752

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(2*k+1)*Binomial[4*n+2, n-k]/(2*n+1), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 22 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(4*n+2, n-k))/(2*n+1);
(Magma) [&+[(2*k+1)*Binomial(4*n+2, n-k)/(2*n+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 22 2025

Crossrefs

Cf. A107026, A390778.

Cf. A002293.

Sequence in context: A390215 A091637 A278429 * A394156 A394149 A341320

Adjacent sequences: A390773 A390774 A390775 * A390777 A390778 A390779

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2025

Status

approved