A354660 a(n) = A354650(n,2*n), for n >= 0.

1, 3, 15, 83, 486, 2937, 18109, 113220, 715122, 4552229, 29156985, 187683795, 1213110600, 7868238588, 51184173036, 333809308696, 2181842704602, 14288748463485, 93737673347185, 615889045662345, 4052198020223430, 26694405836621985, 176052003674681925

Offset: 0

Author

Paul D. Hanna, Jun 02 2022

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A354649, A354650, A354658, A354659.

Programs

PARI

{A354650(n,k) = my(A=[1+y]); for(i=1,n, A = concat(A,0);
A[#A] = polcoeff(y + sum(m=0,sqrtint(2*#A+9), (-1)^m * x^(m*(m-1)/2) * (1 - x^(2*m+1)) * Ser(A)^(m*(m+1)/2) ),#A-1) );
polcoeff(A[n+1],k,y)}
for(n=0,20,print1(A354650(n,2*n),", "))

Formula

a(n) = (-1)^(n+1) * A354649(n,2*n), for n >= 0.

a(n) = A354650(n,2*n), for n >= 0.

a(n) ~ 13 * 3^(3*n - 5/2) / (sqrt(Pi*n) * 2^(2*n)). - Vaclav Kotesovec, Mar 19 2023