A390779 a(n) = (1/(5*n+3)) * Sum_{k=0..n} (5*k+3) * binomial(5*n+3,n-k).

1, 4, 27, 218, 1933, 18168, 177717, 1789872, 18432897, 193200500, 2054074838, 22097723916, 240098265351, 2630922621736, 29040398639928, 322602077778528, 3603875583425961, 40460849092495572, 456280251524230449, 5166114534001602870, 58703595937391436858, 669251733275096962736, 7652675661723407292462

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: g^3/(2-g) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(5*k+3)*Binomial[5*n+3, n-k]/(5*n+3), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 24 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (5*k+3)*binomial(5*n+3, n-k))/(5*n+3);
(Magma) [&+[(5*k+3)*Binomial(5*n+3, n-k)/(5*n+3): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 24 2025

Crossrefs

Cf. A304979, A390777, A390780.

Cf. A002294.

Sequence in context: A190738 A361717 A275607 * A319518 A304045 A365753

Adjacent sequences: A390776 A390777 A390778 * A390780 A390781 A390782

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2025

Status

approved