A354659 A diagonal of triangle A354650: a(n) = A354650(n,n+1), for n >= 0.

1, 3, 30, 390, 5928, 98910, 1757688, 32683680, 628884300, 12428334215, 250940544738, 5156722096422, 107538413657010, 2270751678647100, 48464836803383400, 1044050265679857144, 22675350105240015204, 496034970650911331550, 10920742396832034391590

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, 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+1),", "))

Formula

a(n) = A354649(n,n+1), for n >= 0.

a(n) = A354650(n,n+1), for n >= 0.

a(n) ~ c * d^n / n^2, where d = 24.5759928778699928131449756... and c = 0.35661791857107638456206... - Vaclav Kotesovec, Mar 19 2023