cp's OEIS Frontend

A136733 Square array, read by antidiagonals, where T(n,k) = T(n,k-1) + T(n-1,k+n) for n>0, k>0, such that T(n,0) = T(n-1,n) for n>0 with T(0,k)=1 for k>=0.

%I A136733 #3 Mar 30 2012 18:37:09
%S A136733 1,1,1,3,2,1,18,7,3,1,170,43,12,4,1,2220,403,76,18,5,1,37149,5188,711,
%T A136733 118,25,6,1,758814,85569,9054,1107,170,33,7,1,18301950,1725291,147471,
%U A136733 13986,1605,233,42,8,1,508907970,41145705,2938176,225363,20171,2220,308
%N A136733 Square array, read by antidiagonals, where T(n,k) = T(n,k-1) + T(n-1,k+n) for n>0, k>0, such that T(n,0) = T(n-1,n) for n>0 with T(0,k)=1 for k>=0.
%e A136733 Square array begins:
%e A136733 (1), 1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...];
%e A136733 (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 A136733 (3,7,12), 18, 25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,...;
%e A136733 (18,43,76,118), 170, 233,308,396,498,615,748,898,1066,1253,1460,...;
%e A136733 (170,403,711,1107,1605), 2220, 2968,3866,4932,6185,7645,9333,11271,...;
%e A136733 (2220,5188,9054,13986,20171,27816), 37149, 48420,61902,77892,96712,...;
%e A136733 (37149,85569,147471,225363,322075,440785,585046), 758814, 966477,...;
%e A136733 (758814,1725291,2938176,4441557,6285390,8526057,11226958,14459138), ...;
%e A136733 where the rows are generated as follows.
%e A136733 Start row 0 with all 1's; from then on,
%e A136733 remove the first n+1 terms (shown in parenthesis) from row n
%e A136733 and then take partial sums to yield row n+1.
%e A136733 Note the first upper diagonal forms column 0 and equals A101483:
%e A136733 [1,1,3,18,170,2220,37149,758814,18301950,508907970,16023271660,...]
%e A136733 which equals column 2 of triangle A101479:
%e A136733 1;
%e A136733 1, 1;
%e A136733 1, 1, 1;
%e A136733 3, 2, 1, 1;
%e A136733 19, 9, 3, 1, 1;
%e A136733 191, 70, 18, 4, 1, 1;
%e A136733 2646, 795, 170, 30, 5, 1, 1;
%e A136733 46737, 11961, 2220, 335, 45, 6, 1, 1;
%e A136733 1003150, 224504, 37149, 4984, 581, 63, 7, 1, 1; ...
%e A136733 where row n equals row (n-1) of T^(n-1) with appended '1'.
%o A136733 (PARI) {T(n,k)=if(k<0,0,if(n==0,1,T(n,k-1) + T(n-1,k+n)))}
%Y A136733 Cf. A101479; columns: A101483, A121418, A121421; A121425 (main diagonal); variants: A136730, A136737.
%K A136733 nonn,tabl
%O A136733 0,4
%A A136733 _Paul D. Hanna_, Jan 19 2008