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A205482
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G.f.: exp( Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d ).
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8
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1, 1, 2, 2, 5, 5, 15, 15, 34, 46, 84, 96, 246, 282, 512, 696, 1421, 1713, 3436, 4084, 8227, 10821, 19128, 23258, 48474, 60943, 106780, 139313, 252748, 322577, 600660, 760872, 1365570, 1807979, 3064882, 3951491, 7358684, 9476993, 15962935, 21243381
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OFFSET
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0,3
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COMMENTS
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Note: exp( Sum_{n>=1} x^n/n * Product_{d|n} (1 + x^n)^d ) does not yield an integer series.
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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Logarithmic derivative yields A205483.
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 2*x^3 + 5*x^4 + 5*x^5 + 15*x^6 + 15*x^7 +...
By definition:
log(A(x)) = x*(1+x) + x^2*(1+x^2)*(1+2*x^2)^2/2 + x^3*(1+x^3)*(1+3*x^3)^3/3 + x^4*(1+x^4)*(1+2*x^4)^2*(1+4*x^4)^4/4 + x^5*(1+x^5)*(1+5*x^5)^5/5 + x^6*(1+x^6)*(1+2*x^6)^2*(1+3*x^6)^3*(1+6*x^6)^6/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + x^3/3 + 11*x^4/4 + x^5/5 + 45*x^6/6 + x^7/7 + 59*x^8/8 + 109*x^9/9 + 53*x^10/10 +...+ A205483(n)*x^n/n +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, d*log(1+d*x^m+x*O(x^n)))))), n)}
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CROSSREFS
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Cf. A205483 (log), A205476, A205478, A205480, A205484, A205486, A205488, A205490.
Sequence in context: A106181 A098887 A097438 * A055879 A056470 A056471
Adjacent sequences: A205479 A205480 A205481 * A205483 A205484 A205485
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jan 27 2012
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STATUS
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approved
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