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 A277454 a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^k * k^k. 5
 1, 3, 21, 271, 5065, 122811, 3651997, 128566663, 5227782161, 241072839667, 12430169195941, 708612945554559, 44253858433505497, 3004570398043291819, 220341964157226260525, 17357760973540312138231, 1461813975265547356467745, 131061164660246579394042339 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..351 FORMULA E.g.f.: exp(x)/(1+LambertW(-2*x)). a(n) ~ exp(exp(-1)/2) * 2^n * n^n. MATHEMATICA 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]! PROG (PARI) {a(n) = sum(k=0, n, binomial(n, k)*(2*k)^k)} \\ Seiichi Manyama, Jan 12 2019 CROSSREFS Cf. A086331, A277456. Sequence in context: A375451 A098278 A269938 * A215127 A227820 A336809 Adjacent sequences: A277451 A277452 A277453 * A277455 A277456 A277457 KEYWORD nonn AUTHOR Vaclav Kotesovec, Oct 16 2016 STATUS approved

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Last modified September 14 06:05 EDT 2024. Contains 375911 sequences. (Running on oeis4.)