A361538 Central terms of triangle A361050.

1, 5, 244, 19090, 1839075, 199363606, 23320604384, 2876887986028, 369107300988219, 48807370374419910, 6610055144592717246, 912769451975745598299, 128087096344387852459658, 18219369599509083643661044, 2621701165622760015979876800, 381039123615762485580377457688

Offset: 1

Author

Paul D. Hanna, Mar 18 2023

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..51

Crossrefs

Cf. A361050.

Programs

PARI

{A361050(n,k) = my(A=[0, 1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(y/x - prod(m=1, #A, (1 - x^m) * (1 - x^m*Ser(A)) * (1 - x^(m-1)/Ser(A)) * (1 - x^(2*m-1)*Ser(A)^2) * (1 - x^(2*m-1)/Ser(A)^2) ), #A-4) );
polcoeff(polcoeff(H=Ser(A),n,x),k,y)}
for(n=1, 16, print1(A361050(2*n-1,n-1), ", "))

Formula

a(n) = A361050(2*n-1,n-1) for n >= 1.

a(n) ~ c * d^n / n^2, where d = 166.5794571279985... and c = 0.000249393859904361... - Vaclav Kotesovec, Mar 19 2023