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A110770
Triangle read by rows: T(n,k) = binomial(t(n) - t(k-1),k), where t(j) = j*(j+1)/2; 1<=k<=n.
2
1, 3, 1, 6, 10, 1, 10, 36, 35, 1, 15, 91, 220, 126, 1, 21, 190, 816, 1365, 462, 1, 28, 351, 2300, 7315, 8568, 1716, 1, 36, 595, 5456, 27405, 65780, 54264, 6435, 1, 45, 946, 11480, 82251, 324632, 593775, 346104, 24310, 1, 55, 1431, 22100, 211876, 1221759
OFFSET
1,2
COMMENTS
T(n,1) = t(n) = n*(n+1)/2 = A000217(n); T(n,n) = 1 - Emeric Deutsch, Oct 09 2006
FORMULA
T(n,1) = t(n) = n*(n+1)/2 = A000217(n); T(n,n) = 1. - Emeric Deutsch, Oct 09 2006
EXAMPLE
Triangle starts:
1;
3, 1;
6, 10, 1;
10, 36, 35, 1;
15, 91, 220, 126, 1;
MAPLE
t:=n->n*(n+1)/2: T:=proc(n, k) if k<=n then binomial(t(n)-t(k-1), k) else 0 fi end: for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form. - Emeric Deutsch, Oct 09 2006
MATHEMATICA
Table[Binomial[Binomial[n + 1, 2] - Binomial[k, 2], k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Oct 19 2017 *)
PROG
(PARI) for(n=1, 10, for(k=1, n, print1(binomial(binomial(n+1, 2) - binomial(k, 2), k), ", "))) \\ G. C. Greubel, Oct 19 2017
CROSSREFS
KEYWORD
easy,tabl,nonn
AUTHOR
Amarnath Murthy, Aug 12 2005
EXTENSIONS
More terms from Emeric Deutsch, Oct 09 2006
STATUS
approved