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

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

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

Prog

(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), ", "))

Crossrefs

Cf. A354649, A354650, A354659, A354660.

Sequence in context: A371657 A153853 A067000 * A307650 A168593 A364431

Adjacent sequences: A354655 A354656 A354657 * A354659 A354660 A354661

Keyword

nonn

Author

Paul D. Hanna, Jun 02 2022

Status

approved