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URL: https://oeis.org/A393626

⇱ A393626 - OEIS

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A393626
Main diagonal of rectangular table A393620.
2
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
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), ", "))
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 23 2026
STATUS
approved