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A210443 G.f.: Sum_{n>=0} x^n * (1 + n^2*x)^n / (1 + x + n^2*x^2)^n. 0

%I

%S 1,1,1,6,21,150,962,8640,80220,884520,10709520,140873040,2098741680,

%T 32163828480,568234774800,9957054159360,203333391011520,

%U 4013297314266240,92967912795139200,2041979786688441600,52890421861957680000,1279950952105367942400,36648398470742114918400

%N G.f.: Sum_{n>=0} x^n * (1 + n^2*x)^n / (1 + x + n^2*x^2)^n.

%C a(n) is divisible by ((n-1)/2)! for n>0.

%C Compare to the g.f. of A187741:

%C Sum_{n>=0} x^n*(1+n*x)^n/(1+x+n*x^2)^n = 1/2 + (1+2*x)*Sum_{n>=0} (n+1)!*x^(2*n)/2.

%e G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 21*x^4 + 150*x^5 + 962*x^6 + 8640*x^7 +...

%e where

%e A(x) = 1 + (1+x)*x/(1+x+x^2) + (1+4*x)^2*x^2/(1+x+4*x^2)^2 + (1+9*x)^3*x^3/(1+x+9*x^2)^3 + (1+16*x)^4*x^4/(1+x+16*x^2)^4 + (1+25*x)^5*x^5/(1+x+25*x^2)^5 +...

%o (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+m^2*x)^m/(1+x+m^2*x^2 +x*O(x^n))^m), n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A187741.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Jan 20 2013

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Last modified June 29 06:48 EDT 2022. Contains 354910 sequences. (Running on oeis4.)