cp's OEIS Frontend

A136737 Square array, read by antidiagonals, where T(n,k) = T(n,k-1) + T(n-1,k+n+1) for n>0, k>0, such that T(n,0) = T(n-1,n+1) for n>0 with T(0,k)=1 for k>=0.

%I A136737 #3 Mar 30 2012 18:37:09
%S A136737 1,1,1,4,2,1,30,9,3,1,335,69,15,4,1,4984,769,118,22,5,1,92652,11346,
%T A136737 1317,178,30,6,1,2065146,208914,19311,1995,250,39,7,1,53636520,
%U A136737 4613976,352636,29126,2820,335,49,8,1,1589752230,118840164,7722840,528097,41061
%N A136737 Square array, read by antidiagonals, where T(n,k) = T(n,k-1) + T(n-1,k+n+1) for n>0, k>0, such that T(n,0) = T(n-1,n+1) for n>0 with T(0,k)=1 for k>=0.
%e A136737 Square array begins:
%e A136737 (1,1), 1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...;
%e A136737 (1,2,3), 4, 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,...;
%e A136737 (4,9,15,22), 30, 39,49,60,72,85,99,114,130,147,165,184,204,225,247,...;
%e A136737 (30,69,118,178,250), 335, 434,548,678,825,990,1174,1378,1603,1850,...;
%e A136737 (335,769,1317,1995,2820,3810), 4984, 6362,7965,9815,11935,14349,...;
%e A136737 (4984,11346,19311,29126,41061,55410,72492), 92652, 116262, 143722,...;
%e A136737 (92652,208914,352636,528097,740035,993678,1294776,1649634), 2065146,..;
%e A136737 (2065146,4613976,7722840,11476963,15971180,21310710,27611970,35003430,43626510),..;
%e A136737 where the rows are generated as follows.
%e A136737 Start row 0 with all 1's; from then on,
%e A136737 remove the first n+2 terms (shown in parenthesis) from row n
%e A136737 and then take partial sums to yield row n+1.
%e A136737 Note the second upper diagonal forms column 0 and equals A121413:
%e A136737 [1,1,4,30,335,4984,92652,2065146,53636520,1589752230,52926799310,...].
%e A136737 which equals column 3 of triangle A101479:
%e A136737 1;
%e A136737 1, 1;
%e A136737 1, 1, 1;
%e A136737 3, 2, 1, 1;
%e A136737 19, 9, 3, 1, 1;
%e A136737 191, 70, 18, 4, 1, 1;
%e A136737 2646, 795, 170, 30, 5, 1, 1;
%e A136737 46737, 11961, 2220, 335, 45, 6, 1, 1;
%e A136737 1003150, 224504, 37149, 4984, 581, 63, 7, 1, 1; ...
%e A136737 where row n equals row (n-1) of T^(n-1) with appended '1'.
%o A136737 (PARI) {T(n,k)=if(k<0,0,if(n==0,1,T(n,k-1) + T(n-1,k+n+1)))}
%Y A136737 Cf. A101479; columns: A121413, A121417, A121422; diagonals: A121427, A136741; variants: A136730, A136733.
%K A136737 nonn,tabl
%O A136737 0,4
%A A136737 _Paul D. Hanna_, Jan 19 2008