A390528 a(n) = Sum_{k=0..n} (5*k+1) * binomial(2*n+3*k+1,n-k)/(2*n+3*k+1).

1, 2, 9, 44, 218, 1085, 5413, 27044, 135238, 676679, 3387163, 16959126, 84927555, 425351077, 2130512178, 10672029383, 53459988986, 267808427198, 1341619526546, 6721119008704, 33671229065020, 168686428534968, 845092229746374, 4233798037519318, 21210831646842268

Offset

0,2

Links

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

Formula

G.f.: g/(1-x*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-k]/(2*n+3*k+1), {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (5*k+1)*binomial(2*n+3*k+1, n-k)/(2*n+3*k+1));
(Magma) [&+[(5*k+1)*Binomial(2*n+3*k+1, n-k)/(2*n+3*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 12 2025

Crossrefs

Cf. A026726, A390527.

Cf. A000108, A390520.

Sequence in context: A013981 A390194 A216861 * A199308 A383478 A387677

Adjacent sequences: A390525 A390526 A390527 * A390529 A390530 A390531

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved