A354658 A diagonal of triangle A354650: a(n) = A354650(n,n), for n >= 0.

1, 3, 27, 340, 5070, 83559, 1472261, 27205308, 520974180, 10257025240, 206469879462, 4232227325352, 88073315164471, 1856404180514940, 39560345751767970, 851083806077023888, 18462636758298743712, 403459312929849694791, 8874351725505564788350

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, A354659, A354660.

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,n),", "))

Formula

a(n) = -A354649(n,n), for n >= 0.

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

a(n) ~ c * d^n / n^2, where d = 24.575992877869992813144975... and c = 0.285171824264368179079895... - Vaclav Kotesovec, Jun 08 2022