A390778 a(n) = (1/(4*n+3)) * Sum_{k=0..n} (4*k+3) * binomial(4*n+3,n-k).

1, 4, 23, 152, 1084, 8116, 62866, 499376, 4044740, 33272912, 277200791, 2333900664, 19826702388, 169725523288, 1462620775348, 12677875916128, 110457927237556, 966801715013680, 8496913963019596, 74953578118991584, 663406796335595504, 5889702662262310004

Offset

0,2

Links

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

Formula

G.f.: g^3/(2-g) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[(4*k+3)*Binomial[4*n+3, n-k]/(4*n+3), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 22 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (4*k+3)*binomial(4*n+3, n-k))/(4*n+3);
(Magma) [&+[(4*k+3)*Binomial(4*n+3, n-k)/(4*n+3): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 22 2025

Crossrefs

Cf. A107026, A390776.

Cf. A002293.

Sequence in context: A350480 A193113 A192730 * A246813 A369213 A379088

Adjacent sequences: A390775 A390776 A390777 * A390779 A390780 A390781

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2025

Status

approved