A358954 - OEIS

%I #5 Dec 08 2022 07:34:39

%S 1,4,36,384,4568,57920,768760,10543120,148247390,2125715618,

%T 30965114225,456956616284,6817011617601,102640570550600,

%U 1557716916728198,23804070258610024,365964582592739540,5656501536118793076,87846324474413129008,1370097609728212588634,21451062781643458337802

%N a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(4*n) * (x^n - 2*A(x))^(5*n+1).

%C Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y.

%F G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies:

%F (1) 0 = Sum_{n=-oo..+oo} x^(4*n) * (x^n - 2*A(x))^(5*n+1).

%F (2) 0 = Sum_{n=-oo..+oo} x^(5*n*(n-1)) / (1 - 2*A(x)*x^n)^(5*n-1).

%e G.f.: A(x) = 1 + 4*x + 36*x^2 + 384*x^3 + 4568*x^4 + 57920*x^5 + 768760*x^6 + 10543120*x^7 + 148247390*x^8 + 2125715618*x^9 + 30965114225*x^10 + ...

%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);

%o A[#A] = polcoeff( sum(n=-#A,#A, x^(4*n) * (x^n - 2*Ser(A))^(5*n+1) ), #A-1)/2);A[n+1]}

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

%Y Cf. A355865, A358952, A358953, A358955, A358956, A358957, A358958, A358959.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 07 2022