A346385 a(n) = f(n,n) where f(0,n) = f(n,0) = n^n and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).

1, 3, 19, 151, 1439, 16651, 234651, 3966271, 78504063, 1778555587, 45302809003, 1279960719335, 39697452556959, 1340332692660027, 48929424425580219, 1920103548827941263, 80597817202971009535, 3603262730476776975731, 170923354522784683176267

Offset

0,2

Comments

Main diagonal of square array of Delannoy-like numbers, but with the borders given by n^n instead of 1.

a(n+1)/a(n) ~ e*n (conjectured).

Links

Table of n, a(n) for n=0..18.

Formula

Conjecture:

0 = (310000 - 87575*n^2 + 25110*n^3 - 2015*n^4)*a(n-6)

+ (-3082368 + 190872*n + 1063326*n^2 - 378291*n^3 + 37173*n^4)*a(n-5)

+ (8418604 - 1615685*n - 3834272*n^2 + 1836495*n^3 - 232486*n^4)*a(n-4)

+ (-4087868 + 3360702*n + 3358400*n^2 - 2858550*n^3 + 517914*n^4)*a(n-3)

+ (-3408770 - 992468*n + 1472981*n^2 + 176556 n^3 - 157931*n^4)*a(n-2)

+ (582108 + 205634*n - 541582*n^2 + 120633*n^3 + 12993*n^4)*a(n-1)

+ (-3362 - 20943*n + 37298*n^2 - 12993*n^3)*a(n).

Mathematica

F[0, 0] = 1; F[m_, 0] := m!; F[0, n_] := n^n;
F[m_, n_] := F[m, n] =   F[m - 1 , n ] + F[m , n - 1] +  F[m - 1, n - 1];
Table[F[n, n], {n, 0, 100}]

Crossrefs

Cf. A000312, A001850, A008288, A344576, A346374.

Sequence in context: A324226 A007112 A007111 * A113013 A307489 A323668

Adjacent sequences: A346382 A346383 A346384 * A346386 A346387 A346388

Keyword

nonn

Author

José María Grau Ribas, Jul 14 2021

Status

approved