A390798 a(n) = Sum_{k=0..n} (3*k+2) * binomial(5*n-2*k+2,n-k)/(5*n-2*k+2).

1, 3, 17, 124, 1030, 9251, 87517, 859099, 8669363, 89378119, 937338385, 9968284525, 107246775281, 1165214293500, 12766501347012, 140894107553484, 1564845156329626, 17477561474851094, 196177569785319286, 2211811995984100253, 25037053775934416711, 284438311913461647139

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

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

Mathematica

Table[Sum[(3*k+2)*Binomial[5*n-2*k+2, n-k]/(5*n-2*k+2), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 23 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (3*k+2)*binomial(5*n-2*k+2, n-k)/(5*n-2*k+2));
(Magma) [&+[(3*k+2)*Binomial(5*n-2*k+2, n-k)/(5*n-2*k+2): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 23 2025

Crossrefs

Cf. A118970, A390715, A390721, A390777.

Cf. A002294.

Sequence in context: A216314 A330803 A267736 * A381912 A129115 A246963

Adjacent sequences: A390795 A390796 A390797 * A390799 A390800 A390801

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2025

Status

approved