A366735 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (1 + (-x)^(n-1))^(n+1).

1, 1, 4, 14, 54, 218, 911, 3917, 17235, 77251, 351498, 1619362, 7538944, 35412306, 167626988, 798823025, 3829325596, 18453005188, 89338777895, 434343634600, 2119679152092, 10379998771157, 50989711920778, 251194614740028, 1240735313801625, 6143268099066535

Offset: 0

Author

Paul D. Hanna, Oct 29 2023

Keywords

• nonn

Comments

a(n) = (-1)^n * Sum_{k=0..n} A366730(n,k) * (-1)^k for n >= 0.

Examples

			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 + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A366730, A366731, A366732, A366733, A366734.

Programs

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),", "))

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) ).