cp's OEIS Frontend

A316140 Denominator of the autosequence 2/((n+2)*(n+3)) difference table written by antidiagonals.

%I A316140 #22 Dec 01 2019 23:15:21
%S A316140 3,6,6,10,15,10,15,30,30,15,21,105,70,105,21,28,84,140,140,84,28,36,
%T A316140 126,252,315,252,126,36,45,180,420,630,630,420,180,45,55,495,660,1155,
%U A316140 1386,1155,660,495,55,66,330
%N A316140 Denominator of the autosequence 2/((n+2)*(n+3)) difference table written by antidiagonals.
%H A316140 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%e A316140 Difference table:
%e A316140    1/3,   1/6,    1/10,   1/15,  ...
%e A316140   -1/6,  -1/15,  -1/30,  -2/105, ...
%e A316140    1/10,  1/30,   1/70,   1/140, ...
%e A316140   -1/15, -2/105, -1/140, -1/315, ... .
%e A316140   ...
%e A316140 Table starts:
%e A316140    3   6   10    15    21    28   ...
%e A316140    6  15   30   105    84   126   ...
%e A316140   10  30   70   140   252   420   ...
%e A316140   15 105  140   315   630  1155   ...
%e A316140   21  84  252   630  1386  2772   ...
%e A316140   ...
%e A316140 As a triangle:
%e A316140    3;
%e A316140    6,  6;
%e A316140   10, 15, 10;
%e A316140   15, 30, 30, 15;
%e A316140   ...
%o A316140 (PARI) tabl(nn) = {nn = 2*nn; m = matrix(nn, nn, n, k, if (n==1, 2/((k+1)*(k+2)))); for (n=2, nn, for (k=1, nn-n +1, m[n, k] = m[n-1, k+1] - m[n-1,k];);); nn = nn/2; matrix(nn, nn, n, k, denominator(m[n,k]));} \\ _Michel Marcus_, Jul 05 2018
%Y A316140 Cf. A000217, A003506, A033876? (main diagonal), A059481, A109613.
%K A316140 nonn,frac,tabl,more
%O A316140 0,1
%A A316140 _Paul Curtz_, Jun 25 2018