A354655 Column 2 of triangle A354650: a(n) = A354650(n,2), for n >= 1.

3, 27, 147, 630, 2295, 7476, 22302, 62100, 163260, 409080, 983367, 2280306, 5122026, 11184075, 23806575, 49521456, 100872135, 201558231, 395675475, 764130780, 1453424259, 2725614243, 5044092372, 9219499800, 16655554125, 29759775435, 52623867051

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, A354656.

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),", "))

Formula

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

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