A361556 Central terms of triangle A361550.

1, 5, 61, 1660, 47460, 1621116, 58002140, 2213389940, 87301563690, 3555890156445, 148125509781095, 6292884402884976, 271565202254735207, 11878392121526009800, 525519782174930309205, 23481280252471520720288, 1058270749214634093475910, 48058678036035725619136698

Offset: 0

Author

Paul D. Hanna, Mar 19 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A361550.

Programs

PARI

{A361550(n,k) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x*y - 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-1) );
polcoeff(polcoeff(Ser(A),n,x),k,y)}
for(n=0, 20, print1(A361550(2*n,n), ", "))

Formula

a(n) = A361550(2*n,n) for n >= 0.

a(n) ~ c * d^n / n^2, where d = 51.1751... and c = 0.12624... - Vaclav Kotesovec, Mar 19 2023