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 A336952 E.g.f.: 1 / (1 - x * exp(4*x)). 5
 1, 1, 10, 102, 1336, 22200, 443664, 10334128, 275060608, 8236914048, 274069953280, 10031110907136, 400520747437056, 17324601073921024, 807023462798608384, 40278407730378332160, 2144307919689898491904, 121291661335680615284736, 7264376142168665821741056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..375 FORMULA a(n) = n! * Sum_{k=0..n} (4 * (n-k))^k / k!. a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k * 4^(k-1) * a(n-k). a(n) ~ n! * (4/LambertW(4))^n / (1 + LambertW(4)). - Vaclav Kotesovec, Aug 09 2021 MATHEMATICA nmax = 18; CoefficientList[Series[1/(1 - x Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]! Join[{1}, Table[n! Sum[(4 (n - k))^k/k!, {k, 0, n}], {n, 1, 18}]] a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}] PROG (PARI) seq(n)={ Vec(serlaplace(1 / (1 - x*exp(4*x + O(x^n))))) } \\ Andrew Howroyd, Aug 08 2020 CROSSREFS Column k=4 of A351790. Cf. A002697, A006153, A235328, A326324, A328183, A336950, A336951. Sequence in context: A162666 A061630 A062806 * A331475 A158240 A087393 Adjacent sequences: A336949 A336950 A336951 * A336953 A336954 A336955 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 08 2020 STATUS approved

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Last modified January 28 08:59 EST 2023. Contains 359850 sequences. (Running on oeis4.)