A390479 a(n) = Sum_{k=0..floor(n/4)} (5*k+1) * binomial(2*n-3*k+1,n-4*k)/(2*n-3*k+1).

1, 1, 2, 5, 15, 48, 159, 539, 1860, 6511, 23061, 82482, 297467, 1080451, 3948656, 14509083, 53567875, 198616636, 739234857, 2760847225, 10343227960, 38860033811, 146379004723, 552702113268, 2091506783933, 7930701103721, 30128967199128, 114662186448031

Offset

0,3

Links

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

Formula

G.f.: g/(1-x^4*g^5) where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[(5*k+1)*Binomial[2*n-3*k+1, n-4*k]/(2*n-3*k+1), {k, 0, Floor[n/4]}], {n, 0, 30}] (* Vincenzo Librandi, Nov 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, (5*k+1)*binomial(2*n-3*k+1, n-4*k)/(2*n-3*k+1));
(Magma) [&+[(5*k+1)*Binomial(2*n-3*k+1, n-4*k)/(2*n-3*k+1): k in [0..Floor(n/4)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A081696, A390478, A390480, A390481.

Cf. A000108.

Sequence in context: A301994 A289589 A071739 * A268407 A261003 A365268

Adjacent sequences: A390476 A390477 A390478 * A390480 A390481 A390482

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved