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A336180
a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^3.
3
1, 0, -11, 136, -639, -25624, 1133245, -27431424, 259448833, 17402599792, -1405909697499, 63884679938960, -1830503703899519, -5324845289379264, 5494299851213052685, -496909924804074650624, 30201149245542631276545, -1236819213672144144878752, 5410434345252588202534741
OFFSET
0,3
FORMULA
a(n) = hypergeom([-n, -n, -n], [1, 1], n). - Peter Luschny, Dec 22 2020
MAPLE
a := n -> hypergeom([-n, -n, -n], [1, 1], n):
seq(simplify(a(n)), n=0..18); # Peter Luschny, Dec 22 2020
MATHEMATICA
Array[Function[n, 1 + Sum[(-n)^k Binomial[n, k]^3, {k, n}]], 19, 0] (* Jan Mangaldan, Jul 14 2020 *)
PROG
(PARI) {a(n) = sum(k=0, n, (-n)^k*binomial(n, k)^3)}
CROSSREFS
Main diagonal of A336179.
Sequence in context: A250460 A367245 A157773 * A209487 A227101 A024143
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 10 2020
STATUS
approved