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A336181
a(n) = Sum_{k=0..n} (-2)^k * binomial(n,k)^3.
1
1, -1, -11, 47, 241, -2281, -3779, 104831, -110207, -4415281, 16955269, 161498831, -1252782959, -4376471737, 73606867309, 11876256767, -3715460133887, 9838677757343, 160921055160469, -957644184613393, -5553047963695439, 65231925087461879, 102267746634093469
OFFSET
0,3
COMMENTS
Diagonal of the rational function 1 / (1 + y + z + x*y + y*z - 2*z*x - x*y*z).
Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) + 2*x*y*z).
MATHEMATICA
a[n_] := Sum[(-2)^k * Binomial[n, k]^3, {k, 0, n}]; Array[a, 23, 0] (* Amiram Eldar, Jul 11 2020 *)
PROG
(PARI) {a(n) = sum(k=0, n, (-2)^k*binomial(n, k)^3)}
CROSSREFS
Column k=2 of A336179.
Cf. A206178.
Sequence in context: A267614 A123984 A141282 * A354590 A067355 A138362
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 10 2020
STATUS
approved