A365896 Expansion of e.g.f. exp( Sum_{k>=0} x^(2*k+5) / (2*k+5)! ).
1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 126, 1, 792, 1, 3718, 126127, 15808, 2450449, 64702, 31593277, 489125360, 343746937, 21511079558, 3435303323, 588969369056, 5227461790937, 13006203613950, 434431246754441, 255046847579760, 21684989820772201, 128034458842091862
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..599
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\2, x^(2*k+5)/(2*k+5)!))))
Formula
a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/2)} binomial(n-1,2*k+4) * a(n-2*k-5).
E.g.f.: exp( -x - x^3/6 + sinh(x) ).