A380208 Expansion of e.g.f. exp( (1+3*x)^(1/3) - 1 ).
1, 1, -1, 5, -39, 421, -5809, 97609, -1933455, 44107881, -1138752449, 32820576141, -1044523471991, 36379398867085, -1376300966184689, 56200996031812241, -2463713702730471199, 115400572452587463249, -5751849729149085927425, 303954806150664749166101
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..381
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+3*x)^(1/3)-1)))
Formula
a(n) = Sum_{k=0..n} 3^(n-k) * Stirling1(n,k) * Bell(k).
a(n) = (1/e) * 3^n * n! * Sum_{k>=0} binomial(k/3,n)/k!.
a(0) = 1; a(n) = Sum_{k=1..n} (Product_{j=0..k-1} (-3*j+1)) * binomial(n-1,k-1) * a(n-k).