A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2*k)! * (x/2)^k/k ).
1, 1, 7, 199, 15985, 2810401, 916442551, 497173378087, 416055798439009, 508038355486018945, 867346995542879712871, 2001283948891590010467271, 6070787760933663329315253457, 23660956435620796919900079644449
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (2*k)!*(x/2)^k/k))))
Formula
a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} (2*k)! * a(n-k) / (2^k * (n-k)!).