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A192891 Expansion of g.f.: exp( Sum_{n>=1} 3^n*(Sum_{d|n} d*x^d)^n/n ). 3
1, 3, 9, 45, 153, 702, 2754, 11259, 50058, 224046, 990873, 4304988, 18175185, 77439321, 327135510, 1408297995, 6302244447, 29140976502, 135628856406, 622855827801, 2796140431278, 12364271615628, 54378167114070, 240937280782164, 1080881256295566 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
EXAMPLE
G.f.: A(x) = 1 + 3*x + 9*x^2 + 45*x^3 + 153*x^4 + 702*x^5 + 2754*x^6 + 11259*x^7 +...
where the logarithm of the g.f. begins:
log(A(x)) = 3*x + 9*(x + 2*x^2)^2/2 + 27*(x + 3*x^3)^3/3 + 81*(x + 2*x^2 + 4*x^4)^4/4 + 243*(x + 5*x^5)^5/5 + 729*(x + 2*x^2 + 3*x^3 + 6*x^6)^6/6 + 2187*(x + 7*x^7)^7/7 + 6561*(x + 2*x^2 + 4*x^4 + 8*x^8)^8/8 +...
Explicitly, the logarithmic series begins:
log(A(x)) = 3*x + 9*x^2/2 + 81*x^3/3 + 153*x^4/4 + 1458*x^5/5 + 3645*x^6/6 + 20898*x^7/7 + 100521*x^8/8 + 557685*x^9/9 + 2353374*x^10/10 +...
MATHEMATICA
With[{m = 40}, CoefficientList[Series[Exp[Sum[3^n (Sum[d*x^d, {d, Divisors[n]}])^n/n, {n, 1, m + 2}]], {x, 0, m}], x]] (* G. C. Greubel, Jan 10 2019 *)
PROG
(PARI) {a(n)=local(A); A=exp(sum(m=1, n+1, 3^m*sumdiv(m, d, d*x^d +x*O(x^n))^m/m)); polcoeff(A, n)}
CROSSREFS
Sequence in context: A001902 A224085 A352797 * A364296 A068100 A327648
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 11 2011
STATUS
approved

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Last modified June 17 09:14 EDT 2024. Contains 373444 sequences. (Running on oeis4.)