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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. 5
1, 1, 1, 3, 2, 1, 18, 7, 3, 1, 170, 43, 12, 4, 1, 2220, 403, 76, 18, 5, 1, 37149, 5188, 711, 118, 25, 6, 1, 758814, 85569, 9054, 1107, 170, 33, 7, 1, 18301950, 1725291, 147471, 13986, 1605, 233, 42, 8, 1, 508907970, 41145705, 2938176, 225363, 20171, 2220, 308 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

Square array begins:

(1), 1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...];

(1,2), 3, 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,...;

(3,7,12), 18, 25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,...;

(18,43,76,118), 170, 233,308,396,498,615,748,898,1066,1253,1460,...;

(170,403,711,1107,1605), 2220, 2968,3866,4932,6185,7645,9333,11271,...;

(2220,5188,9054,13986,20171,27816), 37149, 48420,61902,77892,96712,...;

(37149,85569,147471,225363,322075,440785,585046), 758814, 966477,...;

(758814,1725291,2938176,4441557,6285390,8526057,11226958,14459138), ...;

where the rows are generated as follows.

Start row 0 with all 1's; from then on,

remove the first n+1 terms (shown in parenthesis) from row n

and then take partial sums to yield row n+1.

Note the first upper diagonal forms column 0 and equals A101483:

[1,1,3,18,170,2220,37149,758814,18301950,508907970,16023271660,...]

which equals column 2 of triangle A101479:

1;

1, 1;

1, 1, 1;

3, 2, 1, 1;

19, 9, 3, 1, 1;

191, 70, 18, 4, 1, 1;

2646, 795, 170, 30, 5, 1, 1;

46737, 11961, 2220, 335, 45, 6, 1, 1;

1003150, 224504, 37149, 4984, 581, 63, 7, 1, 1; ...

where row n equals row (n-1) of T^(n-1) with appended '1'.

PROG

(PARI) {T(n, k)=if(k<0, 0, if(n==0, 1, T(n, k-1) + T(n-1, k+n)))}

CROSSREFS

Cf. A101479; columns: A101483, A121418, A121421; A121425 (main diagonal); variants: A136730, A136737.

Sequence in context: A088956 A106208 A129377 * A117269 A291080 A107862

Adjacent sequences:  A136730 A136731 A136732 * A136734 A136735 A136736

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jan 19 2008

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)