A389112 Expansion of g^2/(1 - x^2*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 10, 55, 356, 2489, 18345, 140254, 1101902, 8841325, 72141354, 596766853, 4993199792, 42183297986, 359325919409, 3082783675118, 26614271222472, 231037616220573, 2015489636127799, 17659712674654217, 155346364392915100, 1371416834698171121

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (k+2) * binomial(4*n-7*k+2,n-2*k)/(4*n-7*k+2).

Mathematica

Table[Sum[ (k+2)*Binomial[4* n-7*k+2, n-2*k]/(4*n-7*k+2), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (k+2)*binomial(4*n-7*k+2, n-2*k)/(4*n-7*k+2));
(Magma) [&+[(k+2)*Binomial(4*n-7*k+2, n-2*k)/(4*n-7*k+2): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A389653, A390720.

Cf. A390147, A391080, A391082, A391084.

Cf. A002293.

Sequence in context: A268556 A371816 A175935 * A216721 A122826 A320129

Adjacent sequences: A389109 A389110 A389111 * A389113 A389114 A389115

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved