A390710 a(n) = Sum_{k=0..n} (5*k+1) * binomial(4*n+k+1,n-k)/(4*n+k+1).

1, 2, 11, 73, 528, 4017, 31607, 254779, 2091647, 17420270, 146780121, 1248679940, 10708942769, 92478844907, 803403848506, 7016088024023, 61554363004544, 542255447285265, 4794512298020555, 42532684423049866, 378446187960196753, 3376541608977259909

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^4 is the g.f. of A002293.

G.f.: 1/(1 + 1/g - g), where g = 1+x*g^4 is the g.f. of A002293. - Seiichi Manyama, Dec 08 2025

Mathematica

Table[Sum[(5*k+1)*Binomial[4*n+k+1, n-k]/(4*n+k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (5*k+1)*binomial(4*n+k+1, n-k)/(4*n+k+1));
(Magma) [&+[(5*k+1)*Binomial(4*n+k+1, n-k)/(4*n+k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 16 2025

Crossrefs

Cf. A069271, A107026, A390709.

Cf. A002293.

Sequence in context: A323842 A049671 A390740 * A074609 A299786 A335310

Adjacent sequences: A390707 A390708 A390709 * A390711 A390712 A390713

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved