login
A358954
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).
7
1, 4, 36, 384, 4568, 57920, 768760, 10543120, 148247390, 2125715618, 30965114225, 456956616284, 6817011617601, 102640570550600, 1557716916728198, 23804070258610024, 365964582592739540, 5656501536118793076, 87846324474413129008, 1370097609728212588634, 21451062781643458337802
OFFSET
0,2
COMMENTS
Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y.
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies:
(1) 0 = Sum_{n=-oo..+oo} x^(4*n) * (x^n - 2*A(x))^(5*n+1).
(2) 0 = Sum_{n=-oo..+oo} x^(5*n*(n-1)) / (1 - 2*A(x)*x^n)^(5*n-1).
EXAMPLE
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 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(n=-#A, #A, x^(4*n) * (x^n - 2*Ser(A))^(5*n+1) ), #A-1)/2); A[n+1]}
for(n=0, 25, print1(a(n), ", "))
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 07 2022
STATUS
approved