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URL: https://oeis.org/A205477

⇱ A205477 - OEIS

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A205477
L.g.f.: Sum_{n>=1} (x^n/n) * Product_{d|n} (1 + n*x^d/d).
8
1, 3, 4, 7, 11, 12, 29, 15, 49, 43, 100, 100, 157, 45, 299, 159, 273, 795, 761, 307, 830, 2126, 1657, 3276, 1711, 965, 3505, 6405, 1509, 9967, 6976, 9375, 8188, 24483, 8089, 26299, 20795, 29871, 40408, 112475, 51497, 164022, 27650, 83398, 74639, 208015, 280074
OFFSET
1,2
FORMULA
Forms the logarithmic derivative of A205476.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 4*x^3/3 + 7*x^4/4 + 11*x^5/5 + 12*x^6/6 +...
By definition:
L(x) = x*(1+x) + x^2*(1+2*x)*(1+x^2)/2 + x^3*(1+3*x)*(1+x^3)/3 + x^4*(1+4*x)*(1+2*x^2)*(1+x^4)/4 + x^5*(1+5*x)*(1+x^5)/5 + x^6*(1+6*x)*(1+3*x^2)*(1+2*x^3)*(1+x^6)/6 +...
Exponentiation yields the g.f. of A205476:
exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 12*x^6 + 20*x^7 +...
MATHEMATICA
max = 50; s = Sum[(x^(n-1)/n)*Product[1+n*x^d/d, {d, Divisors[n]}], {n, 1, max}] + O[x]^max; CoefficientList[s, x]*Range[max] (* Jean-François Alcover, Dec 23 2015 *)
PROG
(PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, log(1+m*x^d/d+x*O(x^n))))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2012
STATUS
approved