A192860 G.f.: exp( Sum_{n>=1} (Sum_{d|n} d*x^d)^n/n ).

1, 1, 1, 3, 5, 10, 18, 45, 98, 242, 569, 1360, 3101, 6799, 14674, 31297, 66483, 144954, 326150, 787455, 2019266, 5425240, 14793678, 40049832, 105958990, 272562864, 679336804, 1644951169, 3882700822, 8997217790, 20559767303

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 10*x^5 + 18*x^6 + 45*x^7 + ...
where the logarithm of the g.f. begins:
log(A(x)) = x + (x + 2*x^2)^2/2 + (x + 3*x^3)^3/3 + (x + 2*x^2 + 4*x^4)^4/4 + (x + 5*x^5)^5/5 + (x + 2*x^2 + 3*x^3 + 6*x^6)^6/6 + (x + 7*x^7)^7/7 + (x + 2*x^2 + 4*x^4 + 8*x^8)^8/8 + ...
Explicitly, the logarithm yields the l.g.f. of A192859, which begins:
log(A(x)) = x + x^2/2 + 7*x^3/3 + 9*x^4/4 + 26*x^5/5 + 37*x^6/6 + 162*x^7/7 + ...

Mathematica

With[{m = 35}, CoefficientList[Series[Exp[Sum[(Sum[d*x^d, {d, Divisors[n] }])^n/n, {n, 1, m + 2}]], {x, 0, m}], x]] (* G. C. Greubel, Jan 06 2019 *)

Prog

(PARI) {a(n)=local(A); A=exp(sum(m=1, n+1, sumdiv(m, d, d*x^d +x*O(x^n))^m/m)); polcoeff(A, n)}

Crossrefs

Cf. A192859, A192890, A192891.

Sequence in context: A107232 A134522 A001445 * A125750 A018168 A320921

Adjacent sequences: A192857 A192858 A192859 * A192861 A192862 A192863

Keyword

nonn

Author

Paul D. Hanna, Jul 11 2011

Status

approved