A222080 - OEIS

%I #6 Feb 08 2013 01:08:45

%S 1,2,11,92,1013,13726,219919,4057048,84545129,1961698586,50111003987,

%T 1396488977908,42139540225501,1368234341961718,47547441824994647,

%U 1760308790559597104,69151746439874522321,2872358517303945656242,125758844338252841129371,5787515297333376814677004

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

%C A self-convolution of an integer sequence (A222081).

%H Paul D. Hanna, <a href="/A222080/b222080.txt">Table of n, a(n) for n = 0..300</a>

%e The terms satisfy:

%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 +...

%e G.f.: A(x) = 1 + 2*x + 11*x^2 + 92*x^3 + 1013*x^4 + 13726*x^5 + 219919*x^6 + 4057048*x^7 + 84545129*x^8 +...

%e The square-root of g.f. A(x) is an integer series:

%e A(x)^(1/2) = 1 + x + 5*x^2 + 41*x^3 + 453*x^4 + 6205*x^5 + 100649*x^6 + 1878277*x^7 + 39534033*x^8 +...+ A222081(n)*x^n +...

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

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A222081.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 07 2013