A390740 a(n) = Sum_{k=0..n} (-1)^k * (2*k+1) * binomial(4*n-2*k+1,n-k)/(4*n-2*k+1).

1, 0, 2, 11, 73, 516, 3825, 29344, 231050, 1856679, 15166101, 125557710, 1051197507, 8884941534, 75712772251, 649768843803, 5611020122345, 48719510621895, 425088400156118, 3725196584960963, 32773601544458209, 289362605686184615, 2563091445861948236

Offset

0,3

Links

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

Formula

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

Mathematica

Table[Sum[(-1)^k*(2*k+1)*Binomial[4*n -2*k+1, n-k]/(4*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(2*k+1)*binomial(4*n-2*k+1, n-k)/(4*n-2*k+1));
(Magma) [&+[(-1)^k*(2*k+1)*Binomial(4*n-2*k+1, n-k)/(4*n-2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A387982, A390500.

Cf. A002293.

Sequence in context: A363389 A323842 A049671 * A390710 A074609 A299786

Adjacent sequences: A390737 A390738 A390739 * A390741 A390742 A390743

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved