A380307 Expansion of e.g.f. exp( (1+5*x)^(1/5) - 1 ).
1, 1, -3, 25, -335, 6177, -144947, 4128937, -138327615, 5327738497, -231899041475, 11255588133945, -602683483719503, 35288931375293857, -2242963870471014963, 153791777744471484745, -11314787069889491407103, 889087243145447511507969, -74312052321224600661026051
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..355
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+5*x)^(1/5)-1)))
Formula
a(n) = Sum_{k=0..n} 5^(n-k) * Stirling1(n,k) * Bell(k).
a(n) = (1/e) * 5^n * n! * Sum_{k>=0} binomial(k/5,n)/k!.
a(0) = 1; a(n) = Sum_{k=1..n} (Product_{j=0..k-1} (-5*j+1)) * binomial(n-1,k-1) * a(n-k).