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A112036
a(n) = Sum_{k=0..n} k*C(n,k)^3*C(n+k,k), where C := binomial.
1
0, 2, 36, 708, 13800, 275010, 5546016, 112928648, 2316836304, 47818490310, 991809240180, 20655287811972, 431646101898336, 9046910585978538, 190096907348726280, 4003238051096801040, 84468326787457833888, 1785362928126983779374, 37794508394454024115212, 801183789256961484235340
OFFSET
0,2
MATHEMATICA
Table[Sum[k*Binomial[n, k]^3*Binomial[n + k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, k*binomial(n, k)^3*binomial(n+k, k)); \\ Michel Marcus, Mar 10 2016
CROSSREFS
Cf. A112035.
Sequence in context: A124104 A262973 A207832 * A336714 A093530 A001626
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 28 2005
STATUS
approved