A391174 Expansion of g^3/(1 - x*g)^2, where g = 1+x*g^3 is the g.f. of A001764.

1, 5, 23, 110, 553, 2901, 15741, 87711, 499180, 2889929, 16967797, 100801084, 604817298, 3660029145, 22312616163, 136904828226, 844806252567, 5239486909624, 32642297938040, 204190320699481, 1281983971747018, 8075638281836729, 51025930684688731

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(k+1)*(k+3)*Binomial[3*n-2*k+3, n-k]/(3*n-2*k+3), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+1)*(k+3)*binomial(3*n-2*k+3, n-k)/(3*n-2*k+3));
(Magma) [&+[(k+1)*(k+3)*Binomial(3*n-2*k+3, n-k)/(3*n-2*k+3): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 04 2025

Crossrefs

Cf. A001764, A391175, A391176, A391178.

Sequence in context: A192810 A278677 A017974 * A244936 A017975 A360100

Adjacent sequences: A391171 A391172 A391173 * A391175 A391176 A391177

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved