A158096 G.f.: A(x) = exp( Sum_{n>=1} x^n/n * 2^(n^2)/(1 + 2^(n^2)*x^n) ).
1, 2, 6, 188, 16614, 6744492, 11466697660, 80444371592472, 2306003921102413254, 268654794307394089145676, 126765597337037378441876059252, 241678070947171631269022075304755208, 1858395916567280733577643964109494506976348, 57560683587055569906379529978030563771752589955832
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + 2*x + 6*x^2 + 188*x^3 + 16614*x^4 + 6744492*x^5 +... where log(A(x)) = 2/(1 + 2*x)*x + 2^4/(1 + 2^4*x^2)*x^2/2 + 2^9/(1 + 2^9*x^3)*x^3/3 + 2^16/(1 + 2^16*x^4)*x^4/4 + 2^25/(1 + 2^25*x^5)*x^5/5 +... Explicitly, log(A(x)) = 2*x + 8*x^2/2 + 536*x^3/3 + 64960*x^4/4 + 33554592*x^5/5 + 68718964352*x^6/6 + 562949953422208*x^7/7 +...+ A262826(n)*x^n/n +...
Programs
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PARI
{a(n)=if(n==0,1,polcoeff(exp(sum(k=1,n, x^k/k * 2^(k^2)/(1 + 2^(k^2)*x^k +x*O(x^n)))),n))} for(n=0,20,print1(a(n),", ")) -
PARI
{a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, -(-1)^d * 2^(m^2/d) * d) ) +x*O(x^n)), n)} for(n=0,20,print1(a(n),", ")) \\ Paul D. Hanna, Oct 02 2015
Formula
G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} -(-1)^d * 2^(n^2/d) * d ). - Paul D. Hanna, Oct 02 2015
Logarithmic derivative equals A262826.
Comments