A391303 Expansion of g^2/(1 + x^4*g^4), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 7, 30, 142, 722, 3843, 21136, 119156, 684886, 3998441, 23644650, 141331431, 852524958, 5183033965, 31726664930, 195373188850, 1209498757272, 7523063932900, 46991671366922, 294647736792191, 1853899154252454, 11701336203814681, 74068582235696580

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (4*k+2) * binomial(3*n-8*k+2,n-4*k)/(3*n-8*k+2).

Mathematica

Table[ Sum[(-1)^k*(4*k+2)*Binomial[3*n-8*k+2, n-4*k]/(3*n-8*k+2), {k, 0, Floor[n/4]}], {n, 0, 21}] (* Vincenzo Librandi, Dec 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, (-1)^k*(4*k+2)*binomial(3*n-8*k+2, n-4*k)/(3*n-8*k+2));
(Magma) [&+[(-1)^k*(4*k+2)*Binomial(3*n-8*k+2, n-4*k)/(3*n-8*k+2): k in [0..Floor(n/4)]] : n in [0..30] ]; // Vincenzo Librandi, Dec 07 2025

Crossrefs

Cf. A001764, A098746.

Sequence in context: A368936 A260771 A260773 * A368937 A174796 A046648

Adjacent sequences: A391300 A391301 A391302 * A391304 A391305 A391306

Keyword

nonn

Author

Seiichi Manyama, Dec 06 2025

Status

approved