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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). 2
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

Table of n, a(n) for n=0..23.

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 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).

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 February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)