A380158 Expansion of e.g.f. sqrt(exp(-2*x) + 2*x).
1, 0, 2, -4, -4, 64, -8, -3312, 14352, 267776, -3403744, -24119360, 881205184, -593040384, -261913919616, 2567414468864, 83291021050112, -2080429273726976, -22004502593928704, 1526354137528335360, -3870482611349750784, -1112746657730132623360, 18568218633016319670272
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, 2^k*(2*k-1)^(n-k)*binomial(1/2, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} 2^k * (2*k-1)^(n-k) * binomial(1/2,k)/(n-k)!.
a(n) == 0 (mod 2) for n>0.