A346374 a(n) = f(n,n) where f(0,n) = f(n,0) = n! and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).

1, 3, 15, 85, 511, 3221, 21339, 149969, 1133215, 9343525, 85089883, 860979329, 9665236335, 119534610885, 1613648163963, 23564301925713, 369437215969599, 6180713141601765, 109812899448776475, 2063836219057694753, 40894619124091715983, 851891564231714448133

Offset

0,2

Comments

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

All terms are odd.

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

Links

Table of n, a(n) for n=0..21.

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).

Maple

b:= proc(x, y) option remember; `if`(x=0, y!,
      b(x-1, y)+b(sort([x, y-1])[])+b(x-1, y-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..26);  # Alois P. Heinz, Jul 14 2021

Mathematica

F[0, 0] = 1; F[m_, 0] := m!; F[0, 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. A000142, A001850, A008288, A344576.

Sequence in context: A212201 A011900 A371754 * A118342 A084209 A317133

Adjacent sequences: A346371 A346372 A346373 * A346375 A346376 A346377

Keyword

nonn

Author

José María Grau Ribas, Jul 14 2021

Status

approved