A192455 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n*A(-x)^A001650(n+1), where A001650 is defined by "n appears n times (n odd).".
1, 1, 2, 7, 27, 112, 492, 2249, 10580, 50885, 249067, 1236602, 6212563, 31523293, 161317863, 831615320, 4314659345, 22512421092, 118052038100, 621825506334, 3288597601727, 17455485596492, 92958082866815, 496535775228131, 2659574264906443
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 27*x^4 + 112*x^5 + 492*x^6 +... The g.f. satisfies: 1 = A(-x) + x*A(-x)^3 + x^2*A(-x)^3 + x^3*A(-x)^3 + x^4*A(-x)^5 + x^5*A(-x)^5 + x^6*A(-x)^5 + x^7*A(-x)^5 + x^8*A(-x)^5 + x^9*A(-x)^7 +...+ x^n*A(-x)^A001650(n+1) +... where A001650 begins: [1, 3,3,3, 5,5,5,5,5, 7,7,7,7,7,7,7, 9,...]. The g.f. also satisfies: 1-x = (1-x)*A(-x) + x*(1-x^3)*A(-x)^3 + x^4*(1-x^5)*A(-x)^5 + x^9*(1-x^7)*A(-x)^7 + x^16*(1-x^9)*A(-x)^9 +...
Programs
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PARI
{a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(sum(m=1, #A, (-x)^m*Ser(A)^(1+2*sqrtint(m-1)) ), #A)); if(n<0, 0, A[n+1])}
Formula
G.f. satisfies: 1-x = Sum_{n>=1} x^(n^2) * (1-x^(2*n-1)) * A(-x)^(2*n-1).
Comments