A354657 a(n) = A354655(n)/3, for n >= 1.

1, 9, 49, 210, 765, 2492, 7434, 20700, 54420, 136360, 327789, 760102, 1707342, 3728025, 7935525, 16507152, 33624045, 67186077, 131891825, 254710260, 484474753, 908538081, 1681364124, 3073166600, 5551851375, 9919925145, 17541289017, 30714092066, 53279031420

Offset: 1

Author

Paul D. Hanna, Jun 02 2022

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A354649, A354650, A354655.

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=1,30,print1(A354650(n,2)/3,", "))

Formula

a(n) = A354655(n)/3, for n >= 1.

a(n) = A354650(n,2)/3, for n >= 1.

a(n) = (-1)^(n+1) * A354649(n,2)/3, for n >= 1.