A390520 a(n) = Sum_{k=0..n} (5*k+1) * binomial(3*n+2*k+1,n-k)/(3*n+2*k+1).

1, 2, 10, 57, 342, 2110, 13249, 84208, 539976, 3486023, 22625320, 147475993, 964673641, 6328806696, 41624721918, 274356449261, 1811713553522, 11983214913061, 79374872776171, 526439830850299, 3495517243290210, 23233835802588171, 154573129846995805, 1029232283267545365

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^3 is the g.f. of A001764.

Mathematica

Table[Sum[(5*k+1)*Binomial[3*n+2*k+1, n-k]/(3*n+2*k+1), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 10 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (5*k+1)*binomial(3*n+2*k+1, n-k)/(3*n+2*k+1));
(Magma) [&+[(5*k+1)*Binomial(3*n+2*k+1, n-k)/(3*n+2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 10 2025

Crossrefs

Cf. A047098, A390519.

Cf. A001764.

Sequence in context: A235321 A364306 A371770 * A369487 A391080 A248403

Adjacent sequences: A390517 A390518 A390519 * A390521 A390522 A390523

Keyword

nonn

Author

Seiichi Manyama, Nov 08 2025

Status

approved