A390280 Expansion of g/(1 - x^2*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 5, 24, 150, 1024, 7440, 56309, 439077, 3502514, 28445790, 234410123, 1955074718, 16472105843, 139986966392, 1198576541306, 10329263410829, 89528006394842, 779924994233080, 6825191955252373, 59971491967474919, 528897755129195762, 4680024482332097320

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(4*n-7*k+1,n-2*k)/(4*n-7*k+1).

Mathematica

Table[Sum[ (k+1)*Binomial[4* n-7*k+1, n-2*k]/(4*n-7*k+1), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (k+1)*binomial(4*n-7*k+1, n-2*k)/(4*n-7*k+1));
(Magma) [&+[(k+1)*Binomial(4*n-7*k+1, n-2*k)/(4*n-7*k+1): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A109963, A391097, A391099, A391104.

Cf. A002293, A389112, A391102.

Sequence in context: A228067 A372138 A322208 * A241134 A340358 A009424

Adjacent sequences: A390277 A390278 A390279 * A390281 A390282 A390283

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2025

Status

approved