A375175 Expansion of e.g.f. exp( (exp( (exp(4*x) - 1)/2 ) - 1)/2 ).
1, 1, 7, 63, 713, 9753, 156111, 2858103, 58845105, 1344371793, 33713484151, 919838859151, 27105053988793, 857310780134825, 28953291147179007, 1039373409620929671, 39505610599553955809, 1584411299793530257697, 66846625774893448843879
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Bell Polynomial.
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((exp((exp(4*x)-1)/2)-1)/2)))
Formula
a(n) = Sum_{k=0..n} 4^(n-k) * Stirling2(n,k) * A004211(k) = 4^n * Sum_{k=0..n} (1/2)^k * Stirling2(n,k) * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.