|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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)!.
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|