A205488 G.f.: exp( Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^n)^d ).

1, 1, 2, 3, 7, 9, 26, 32, 85, 129, 293, 389, 1105, 1426, 3242, 5121, 11405, 15790, 37704, 52289, 118470, 181770, 373257, 543137, 1250814, 1796474, 3713201, 5790866, 11919993, 17663189, 37445802, 55499537, 113653306, 177038255, 347919239, 529686395, 1091858128

Offset

0,3

Comments

Note: exp( Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - x^n)^d ) does not yield an integer series.

Links

Table of n, a(n) for n=0..36.

Formula

Logarithmic derivative yields A205489.

Example

 G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 9*x^5 + 26*x^6 + 32*x^7 +...
By definition:
log(A(x)) = x/(1-x) + (x^2/2)/((1-x^2)*(1-2*x^2)^2) + (x^3/3)/((1-x^3)*(1-3*x^3)^3) + (x^4/4)/((1-x^4)*(1-2*x^4)^2*(1-4*x^4)^4) + (x^5/5)/((1-x^5)*(1-5*x^5)^5) + (x^6/6)/((1-x^6)*(1-2*x^6)^2*(1-3*x^6)^3*(1-6*x^6)^6) +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 4*x^3/3 + 15*x^4/4 + 6*x^5/5 + 78*x^6/6 + 8*x^7/7 + 247*x^8/8 + 202*x^9/9 + 708*x^10/10 +...+ A205489(n)*x^n/n +...

Prog

 (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)}

Crossrefs

Cf. A205489 (log), A205476, A205478, A205480, A205482, A205484, A205486, A205490.

Sequence in context: A250267 A333517 A207643 * A299437 A255393 A248037

Adjacent sequences: A205485 A205486 A205487 * A205489 A205490 A205491

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved