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A352842
Expansion of e.g.f. exp(Sum_{k>=1} sigma_k(k) * x^k).
3
1, 1, 11, 199, 7585, 427961, 37901851, 4526311231, 729098029409, 149311985624785, 38243144308952971, 11913301283967428951, 4445712423354285230401, 1954806416110914007773769, 1000799932457357582959443035, 589931632494798210345741193231
OFFSET
0,3
LINKS
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} k * sigma_k(k) * a(n-k)/(n-k)!.
a(n) ~ n! * n^n. - Vaclav Kotesovec, Apr 15 2022
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(Sum[DivisorSigma[k, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sigma(k, k)*x^k))))
(PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*sigma(k, k)*a(n-k)/(n-k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2022
STATUS
approved