A366736 Central terms of triangle A366730.

1, -2, 14, -176, 2615, -42444, 734310, -13332898, 251087228, -4863520344, 96340129818, -1943639738074, 39815238143374, -826201916477272, 17334983283537509, -367213838120451038, 7844257467257818627, -168807941163188191336, 3656662240133060807499, -79675906058698383705100

Offset: 0

Author

Paul D. Hanna, Oct 30 2023

Keywords

• sign

Comments

This sequence is defined by a(n) = [x^(2*n)*y^n] F(x,y) for n >= 0, where F(x,y) satisfies 0 = Sum_{n=-oo..+oo} x^n * F(x,y)^n * (y - x^(n-1))^(n+1), and F(x,y) is the g.f. of triangle A366730.

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A366730, A366731, A366732, A366733, A366734, A366735.

Programs

PARI

{A366730(n,k) = my(A=[1]); for(i=1,n, A = concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (y - x^(n-1))^(n+1) ), #A-2)); polcoeff(A[n+1],k)}
for(n=0,20, print1(A366730(2*n,n),", "))

Formula

a(n) = A366730(2*n,n) for n >= 0.