OFFSET
0,3
COMMENTS
a(n) = (-1)^n * Sum_{k=0..n} A366730(n,k) * (-1)^k for n >= 0.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
(1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (1 + (-x)^(n-1))^(n+1).
(2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 + (-x)^(n+1))^(n-1) ).
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 14*x^3 + 54*x^4 + 218*x^5 + 911*x^6 + 3917*x^7 + 17235*x^8 + 77251*x^9 + 351498*x^10 + 1619362*x^11 + 7538944*x^12 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff( sum(n=-#A, #A, x^n * Ser(A)^n * (1 + (-x)^(n-1))^(n+1) ), #A-2)); H=A; A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 29 2023
STATUS
approved