A391082 Expansion of g^2/(1 - x^2*g^4), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 10, 58, 380, 2676, 19791, 151614, 1192665, 9577824, 78198892, 647171036, 5416828315, 45774745982, 390004614958, 3346590453746, 28896092544580, 250877633913754, 2188801543939393, 19180039324918600, 168733649257643875, 1489705683122714176

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[ (2*k+1)*Binomial[4* n-4*k+2, n-2*k]/(2*n-2*k+1), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(4*n-4*k+2, n-2*k)/(2*n-2*k+1));
(Magma) [&+[(2*k+1)*Binomial(4*n-4*k+2, n-2*k)/(2*n-2*k+1): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A390776, A391083.

Cf. A389112, A390147, A391080, A391084.

Cf. A002293.

Sequence in context: A075870 A074608 A086871 * A108450 A293111 A112369

Adjacent sequences: A391079 A391080 A391081 * A391083 A391084 A391085

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved