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A372320
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Expansion of e.g.f. -exp( x + LambertW(-2*x)/2 ).
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3
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-1, 0, 4, 36, 464, 8560, 206112, 6104896, 214376192, 8701657344, 400748710400, 20642974511104, 1175888936749056, 73389707156586496, 4980134850525986816, 365062349226075463680, 28747688571714736160768, 2420266280392895064506368
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (2*k-1)^(k-1) * binomial(n,k).
G.f.: Sum_{k>=0} (2*k-1)^(k-1) * x^k / (1-x)^(k+1).
a(n) ~ 2^(n-1) * n^(n-1) * exp((exp(-1) - 1)/2). - Vaclav Kotesovec, May 06 2024
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-2*x)/2)))
(PARI) a(n) = sum(k=0, n, (2*k-1)^(k-1)*binomial(n, k));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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