A245928 G.f. satisfies: A(x) = 1 + x*AGM(A(x)^4, A(-x)^4).
1, 1, 0, 2, 0, 5, 0, 12, 0, 20, 0, -30, 0, -546, 0, -3672, 0, -18796, 0, -79640, 0, -270955, 0, -584340, 0, 903396, 0, 20471948, 0, 155046180, 0, 872787888, 0, 4012121412, 0, 14728928136, 0, 34982326212, 0, -40695186320, 0, -1194336566976, 0, -9612277504606, 0, -56604770338290, 0
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 2*x^3 + 5*x^5 + 12*x^7 + 20*x^9 - 30*x^11 - 546*x^13 -... where AGM(A(x)^4,A(-x)^4) = 1 + 2*x^2 + 5*x^4 + 12*x^6 + 20*x^8 - 30*x^10 - 546*x^12 -... RELATED SERIES: A(x)^2 = 1 + 2*x + x^2 + 4*x^3 + 4*x^4 + 10*x^5 + 14*x^6 + 24*x^7 + 44*x^8 +... A(x)^4 = 1 + 4*x + 6*x^2 + 12*x^3 + 25*x^4 + 44*x^5 + 92*x^6 + 156*x^7 + 308*x^8 +... (A(x)^4 + A(-x)^4)/2 = 1 + 6*x^2 + 25*x^4 + 92*x^6 + 308*x^8 + 878*x^10 + 1614*x^12 -... A(x)^2*A(-x)^2 = 1 - 2*x^2 - 7*x^4 - 20*x^6 - 44*x^8 - 26*x^10 + 494*x^12 + 4152*x^14 +...
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..350
Programs
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PARI
{a(n)=local(A=1+x);for(i=1,n,A=1 + x*agm(A^4,subst(A,x,-x +x*O(x^n))^4));polcoeff(A,n)} for(n=0,40,print1(a(n),", "))
Formula
G.f. satisfies: A(x) = 1 + x*AGM( (A(x)^4 + A(-x)^4)/2, A(x)^2*A(-x)^2 ).
Comments