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 A295739 Expansion of e.g.f. exp(Sum_{k>=1} d(k)*x^k/k!), where d(k) is the number of divisors of k (A000005). 7
 1, 1, 3, 9, 36, 158, 802, 4434, 26978, 176637, 1243528, 9316519, 74065506, 621187700, 5480130494, 50662481722, 489552042241, 4931215686119, 51668848043427, 561981734692781, 6333882472789914, 73850048237680936, 889461218944314524, 11051067390893340510 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Exponential transform of A000005. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..553 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Exponential Transform FORMULA E.g.f.: exp(Sum_{k>=1} A000005(k)*x^k/k!). a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A000005(k)*a(n-k). MAPLE a:=series(exp(add(tau(k)*x^k/k!, k=1..100)), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019 MATHEMATICA nmax = 23; CoefficientList[Series[Exp[Sum[DivisorSigma[0, k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] DivisorSigma[0, k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}] CROSSREFS Cf. A000005, A006171, A028342, A038200, A129921, A160399, A274804, A294363. Sequence in context: A276368 A058540 A245888 * A156016 A032314 A144352 Adjacent sequences:  A295736 A295737 A295738 * A295740 A295741 A295742 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 26 2017 STATUS approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)