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A205544
G.f.: Sum_{n>=0} x^n / Product_{d|n} (1-d*x).
0
1, 1, 2, 5, 13, 37, 114, 384, 1405, 5542, 23395, 105140, 501157, 2525266, 13403833, 74657894, 434731997, 2637999706, 16641634913, 108969490492, 739936135562, 5207151341656, 37955824652053, 286365580836781, 2234228542466676, 18006401603873750
OFFSET
0,3
COMMENTS
Compare g.f. to the o.g.f. of Bell numbers (A000110): Sum_{n>=0} x^n/Product_{k=1..n} (1-k*x).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 13*x^4 + 37*x^5 + 114*x^6 + 384*x^7 +...
By definition:
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)) + x^3/((1-x)*(1-3*x)) + x^4/((1-x)*(1-2*x)*(1-4*x)) + x^5/((1-x)*(1-5*x)) + x^6/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)) +...
PROG
(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*exp(-sumdiv(m, d, log(1-d*x +x*O(x^n))))), n)}
CROSSREFS
Sequence in context: A119495 A148301 A339039 * A149855 A149856 A320175
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 28 2012
STATUS
approved