A373683 Expansion of e.g.f. exp(x / (1 - x^2)) / (1 - x^2).
1, 1, 3, 13, 61, 441, 3031, 28813, 267513, 3088081, 36278731, 491262861, 6962025973, 108395586313, 1791145742751, 31601369155021, 594291393830641, 11740929829286433, 246910933786777363, 5406641472165854221, 125497950720670828461, 3018786042678264770521
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, binomial(n-k, k)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n-k,k)/(n-2*k)!.
a(n) == 1 (mod 2).