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%I #5 Feb 07 2013 21:55:59
%S 1,1,5,41,453,6205,100649,1878277,39534033,924986401,23790991061,
%T 666732284009,20211529694661,658743175016461,22964324182662569,
%U 852450674859207605,33563386167190876321,1396839898167086931137,61260669590285253202981,2823455397312949805962921
%N Self-convolution equals A222080.
%C A222080 satisfies: 1 = Sum_{n>=0} A222080(n)*x^n*(1 - (2*n+1)*x)^2.
%H Paul D. Hanna, <a href="/A222081/b222081.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) == 1 (mod 4).
%F Limit A222080(n)/a(n) = 2.
%e G.f.: A(x) = 1 + x + 5*x^2 + 41*x^3 + 453*x^4 + 6205*x^5 + 100649*x^6 +...
%e where
%e A(x)^2 = 1 + 2*x + 11*x^2 + 92*x^3 + 1013*x^4 + 13726*x^5 + 219919*x^6 +...+ A222080(n)*x^n +...
%e such that A222080 satisfies:
%e 1 = (1-x)^2 + 2*x*(1-3*x)^2 + 11*x^2*(1-5*x)^2 + 92*x^3*(1-7*x)^2 + 1013*x^4*(1-9*x)^2 + 13726*x^5*(1-11*x)^2 + 219919*x^6*(1-13*x)^2 +...+ A222080(n)*x^n*(1 - (2*n+1)*x)^2 +...
%o (PARI) {A222080(n)=polcoeff(1-sum(m=0, n-1, A222080(m)*x^m*(1-(2*m+1)*x+x*O(x^n))^2), n)}
%o {a(n)=polcoeff(sqrt(sum(k=0,n,A222080(k)*x^k+x*O(x^n))),n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A222080.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 07 2013
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