A380133 Expansion of e.g.f. sqrt(1 + 2*x*exp(x)).
1, 1, 1, 0, 1, 0, -9, 70, -335, 504, 11935, -182094, 1525833, -4911764, -99495473, 2430329070, -29988416159, 158542630224, 2868272912511, -102775471991126, 1714422613948345, -13166449628575404, -209400601689898289, 10598981162761786950, -227206614609529433199
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(1/2, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(1/2,k)/(n-k)!.