A047675 Square array a(n,k) read by antidiagonals: a(n,1)=n, a(1,k)=k, a(n,k) = a(n-1,k-1)*a(n-1,k)*a(n,k-1).

1, 2, 2, 3, 4, 3, 4, 24, 24, 4, 5, 288, 2304, 288, 5, 6, 5760, 15925248, 15925248, 5760, 6, 7, 172800, 26418075402240, 584325558976905216, 26418075402240, 172800, 7, 8, 7257600, 26294650153960734720000, 245834178389044369818454697074564792320

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• nice
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..70

Crossrefs

Main diagonal is A047676. Rows give A047677, A047678.

Programs

Maple

A047675 := proc(n,k) option remember; if n = 1 then k; elif k = 1 then n; else A047675(n-1,k-1)*A047675(n,k-1)*A047675(n-1,k); fi; end;

Mathematica

a[n_, 1] := n; a[1, k_] := k; a[n_, k_] := a[n, k] = a[n-1, k-1]*a[n-1, k]*a[n, k-1]; Table[a[n-k+1, k], {n, 1, 8}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 08 2013 *)