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A358651
a(n) = n!*Sum_{m=1..floor(n/2)} 1/(m^2*binomial(n-m,m)).
0
0, 0, 2, 3, 14, 40, 254, 1106, 9400, 56232, 607392, 4685472, 61485984, 585235872, 9014205888, 102480586560, 1806461775360, 23934358033920, 473963802485760, 7180611912944640, 157539651679641600, 2688528843644313600, 64654185117092659200
OFFSET
0,3
FORMULA
E.g.f.: (Li_2(x+x^2-x^3) - Li_2(x))/(1-x), where Li_2(x) is the dilogarithm.
MATHEMATICA
a[n_] := n! * Sum[1/(m^2*(Binomial[n - m, m])), {m, 1, Floor[n/2]}]; Array[a, 21, 2] (* Amiram Eldar, Nov 25 2022 *)
PROG
(Maxima)
a(n):=sum(1/(m^2*(binomial(n-m, m))), m, 1, floor((n)/2));
(PARI) a(n) = n!*sum(m=1, n\2, 1/(m^2*binomial(n-m, m))); \\ Michel Marcus, Nov 25 2022
CROSSREFS
Sequence in context: A329442 A281486 A185895 * A128849 A294495 A188289
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 25 2022
STATUS
approved