A177753 G.f.: A(x) = exp( Sum_{n>=1} (n+1)*A177752(n)*x^n/n - x ).
1, 1, 2, 11, 140, 3102, 102713, 4698780, 283041208, 21704073515, 2064570182438, 238616651727324, 32939304929679337, 5353248306115060288, 1011770777921642230227, 220048666117424880696401
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 140*x^4 + 3102*x^5 +... Compare the series S(x) = d/dx x^2/Series_Reversion(x*A(x)): S(x) = 1 + 2*x + 3*x^2 + 28*x^3 + 515*x^4 + 14766*x^5 + 596652*x^6 +... to the logarithmic derivative: A'(x)/A(x) = 1 + 3*x + 28*x^2 + 515*x^3 + 14766*x^4 + 596652*x^5 +... and also to the g.f. G(x) of A177752: G(x) = 1 + x + x^2 + 7*x^3 + 103*x^4 + 2461*x^5 + 85236*x^6 +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..250
Programs
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PARI
{a(n)=local(A=1+x+sum(m=2,n-1,a(m)*x^m));A=(1/x)*serreverse(x^2/intformal(1+x+x*deriv(A)/(A+x*O(x^n))));if(n<0,0,if(n<2,1,polcoeff((n+1)*A,n)))}
Formula
G.f. satisfies: 1+x + x*A'(x)/A(x) = d/dx x^2/Series_Reversion(x*A(x)).
a(n) ~ c * (n!)^2 / sqrt(n), where c = 0.500612869985729164508780668394780439... - Vaclav Kotesovec, Oct 18 2017
Comments