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).
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
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Jul 14 2021
STATUS
approved