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A277454
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a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^k * k^k.
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5
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1, 3, 21, 271, 5065, 122811, 3651997, 128566663, 5227782161, 241072839667, 12430169195941, 708612945554559, 44253858433505497, 3004570398043291819, 220341964157226260525, 17357760973540312138231, 1461813975265547356467745, 131061164660246579394042339
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..351
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FORMULA
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E.g.f.: exp(x)/(1+LambertW(-2*x)).
a(n) ~ exp(exp(-1)/2) * 2^n * n^n.
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MATHEMATICA
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Table[1+Sum[Binomial[n, k]*2^k*k^k, {k, 1, n}], {n, 0, 20}]
CoefficientList[Series[E^x/(1+LambertW[-2*x]), {x, 0, 20}], x] * Range[0, 20]!
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(n, k)*(2*k)^k)} \\ Seiichi Manyama, Jan 12 2019
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CROSSREFS
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Cf. A086331, A277456.
Sequence in context: A221094 A098278 A269938 * A215127 A227820 A336809
Adjacent sequences: A277451 A277452 A277453 * A277455 A277456 A277457
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Oct 16 2016
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STATUS
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approved
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