A354656 Column 3 of triangle A354650: a(n) = A354650(n,3), for n >= 1.

1, 30, 340, 2530, 14595, 70737, 301070, 1157820, 4100785, 13563010, 42321840, 125586440, 356621070, 973989030, 2569116330, 6567458520, 16317741975, 39504992395, 93390535840, 215983566780, 489454806785, 1088433416785, 2378160809610, 5111208572940, 10816601842950

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, A354657.

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,3),", "))

Formula

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

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