A393626 Main diagonal of rectangular table A393620.

1, 1, 6, 122, 5078, 345505, 34213860, 4603101446, 804243898482, 176730623264183, 47683198300431882, 15499319876511204976, 5976325729384679918608, 2698353156235609436839802, 1410878142725377941788380644, 846101644437201951350608133454, 577059618761577086070620051571226, 444244804743417659840852107522214683

Offset

0,3

Comments

The n-th row o.g.f. R(n,x) of rectangular table A393620 satisfies: [x^m] exp( m*(m+1) * x*R(n,x)^n ) / R(n,x)^(m+1) = 0 for m >= 1, n >= 0. This sequence is therefore defined by a(n) = [x^n] R(n,x), starting with a(0) = A337458(0), a(1) = A393621(1), a(2) = A393622(2), a(3) = A393623(3), a(4) = A393624(4), and a(5) = A393625(5).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..250

Formula

a(n) ~ c * n^(2*n + 1/2) / exp(n), where c = 4.0374... - Vaclav Kotesovec, Feb 25 2026

Prog

(PARI) {A393620(n, k) = my(A=[1], m); for(i=1, k, A=concat(A, 0); m=#A-1; A[m+1] = Vec( exp(m*(m+1)*x*Ser(A)^n +x*O(x^m)) / Ser(A)^(m+1) )[m+1]/(m+1) ); A[k+1]}
for(n=0, 20, print1( A393620(n, n), ", "))

Crossrefs

Cf. A393620, A337458, A393621, A393622, A393623, A393624, A393625.

Sequence in context: A249168 A360576 A138572 * A356199 A078261 A239752

Adjacent sequences: A393623 A393624 A393625 * A393627 A393628 A393629

Keyword

nonn

Author

Paul D. Hanna, Feb 23 2026

Status

approved