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A361776
Expansion of g.f. A(x) satisfying x*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^n * A(x)^n * (A(x)^n + x^n)^n.
2
1, 1, 6, 33, 198, 1204, 7522, 48270, 316281, 2110018, 14293494, 98054885, 679735489, 4753912524, 33504984427, 237767467381, 1697719206178, 12188097989345, 87913304459342, 636736565338008, 4628839922257617, 33767007201285762, 247145222148251103, 1814452818239003585
OFFSET
0,3
COMMENTS
First negative term is a(51) = -47152346702575235627205086026135269902810693.
LINKS
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
(1) x*A(x) = Sum_{n=-oo..+oo} (-1)^n * (x*A(x))^n * (A(x)^n + x^n)^n.
(2) x*A(x) = Sum_{n=-oo..+oo} (-1)^n * (x*A(x))^(n*(n-1)) / (A(x)^n + x^n)^n.
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 33*x^3 + 198*x^4 + 1204*x^5 + 7522*x^6 + 48270*x^7 + 316281*x^8 + 2110018*x^9 + 14293494*x^10 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff(x*Ser(A) - sum(m=-#A, #A, (-1)^m * x^m * Ser(A)^m * (Ser(A)^m + x^m)^m ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Cf. A361775.
Sequence in context: A260774 A218182 A093964 * A193665 A097662 A366200
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 08 2023
STATUS
approved