# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a205814 Showing 1-1 of 1 %I A205814 #14 Feb 12 2018 21:05:42 %S A205814 1,1,9,54,482,4239,55561,785554,14133055,285547760,6666380256, %T A205814 172748192767,4974178683908,156462697434990,5354832107694444, %U A205814 197710292330150160,7839473395324929677,332071887435037103895,14968498613432649146050,715294449027151380463781 %N A205814 G.f.: Product_{n>=1} [ (1 - 2^n*x^n) / (1 - (n+2)^n*x^n) ]^(1/n). %C A205814 Here sigma(n,k) equals the sum of the k-th powers of the divisors of n. %H A205814 Vaclav Kotesovec, Table of n, a(n) for n = 0..380 %F A205814 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=1..n} binomial(n,k) * sigma(n,k) * 2^(n-k) ). %F A205814 a(n) ~ exp(2) * n^(n-1). - _Vaclav Kotesovec_, Oct 08 2016 %e A205814 G.f.: A(x) = 1 + x + 9*x^2 + 54*x^3 + 482*x^4 + 4239*x^5 + 55561*x^6 +... %e A205814 where the g.f. equals the product: %e A205814 A(x) = (1-2*x)/(1-3*x) * ((1-2^2*x^2)/(1-4^2*x^2))^(1/2) * ((1-2^3*x^3)/(1-5^3*x^3))^(1/3) * ((1-2^4*x^4)/(1-6^4*x^4))^(1/4) * ((1-2^5*x^5)/(1-7^5*x^5))^(1/5) *... %e A205814 The logarithm equals the l.g.f. of A205815: %e A205814 log(A(x)) = x + 17*x^2/2 + 136*x^3/3 + 1585*x^4/4 + 16986*x^5/5 +... %o A205814 (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*sum(k=1, m, binomial(m, k)*sigma(m, k)*2^(m-k))+x*O(x^n))), n)} %o A205814 (PARI) {a(n)=polcoeff(prod(k=1, n, ((1-2^k*x^k)/(1-(k+2)^k*x^k +x*O(x^n)))^(1/k)), n)} %Y A205814 Cf. A205815 (log), A205811, A023881. %K A205814 nonn %O A205814 0,3 %A A205814 _Paul D. Hanna_, Feb 01 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE