A356819 Expansion of e.g.f. exp(-x * exp(2*x)).
1, -1, -3, -1, 41, 239, 229, -8401, -87151, -324577, 3238541, 70271519, 601086265, 142860431, -81504662539, -1393683935281, -10777424809951, 63537986981183, 3552608426329117, 60283510555017023, 441644419610814281, -6191820436867600081
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*exp(2*x)))) -
PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-2*k*x)^(k+1))) -
PARI
a(n) = sum(k=0, n, (-1)^k*(2*k)^(n-k)*binomial(n, k));
Formula
G.f.: Sum_{k>=0} (-x)^k / (1 - 2*k*x)^(k+1).
a(n) = Sum_{k=0..n} (-1)^k * (2*k)^(n-k) * binomial(n,k).