Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Jun 24 2017 13:45:16
%S 1,2,2,3,4,3,4,24,24,4,5,288,2304,288,5,6,5760,15925248,15925248,5760,
%T 6,7,172800,26418075402240,584325558976905216,26418075402240,172800,7,
%U 8,7257600,26294650153960734720000,245834178389044369818454697074564792320
%N 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).
%H Vincenzo Librandi, <a href="/A047675/b047675.txt">Table of n, a(n) for n = 1..70</a>
%p 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;
%t 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 *)
%Y Main diagonal is A047676. Rows give A047677, A047678.
%K nonn,tabl,nice,easy
%O 1,2
%A _N. J. A. Sloane_