A361538 Central terms of triangle A361050.

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

Offset

1,2

Links

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

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

Prog

(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), ", "))

Crossrefs

Cf. A361050.

Sequence in context: A317165 A327582 A144999 * A215910 A097323 A166943

Adjacent sequences: A361535 A361536 A361537 * A361539 A361540 A361541

Keyword

nonn

Author

Paul D. Hanna, Mar 18 2023

Status

approved