A380213 Expansion of e.g.f. exp( 1/(1-2*x)^(5/2) - 1 ).
1, 5, 60, 965, 19315, 459420, 12597775, 389902175, 13410470700, 506509866575, 20811096098725, 923085833362500, 43921261488000625, 2229827043134538125, 120239258292160027500, 6859351794101350278125, 412554191158956599261875, 26080572238227541202917500
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1/(1-2*x)^(5/2)-1)))
Formula
a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * |Stirling1(n,k)| * Bell(k).
a(n) = (1/e) * (-2)^n * n! * Sum_{k>=0} binomial(-5*k/2,n)/k!.