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A176123
Irregular triangle, read by rows, T(n, k) = binomial(n-(k-1),k-1), 1 <= k <= floor(n/2-1).
1
1, 1, 1, 5, 1, 6, 1, 7, 15, 1, 8, 21, 1, 9, 28, 35, 1, 10, 36, 56, 1, 11, 45, 84, 70, 1, 12, 55, 120, 126, 1, 13, 66, 165, 210, 126, 1, 14, 78, 220, 330, 252, 1, 15, 91, 286, 495, 462, 210, 1, 16, 105, 364, 715, 792, 462, 1, 17, 120, 455, 1001, 1287, 924, 330, 1, 18, 136, 560, 1365, 2002, 1716, 792
OFFSET
4,4
COMMENTS
The row sum is A099572 which has limiting ratio of (1+sqrt(5))/2.
This is Pascal's triangle (A007318) read along upward sloping diagonals and truncated.
EXAMPLE
Triangle begins as:
1;
1;
1, 5;
1, 6;
1, 7, 15;
1, 8, 21;
1, 9, 28, 35;
1, 10, 36, 56;
1, 11, 45, 84, 70;
1, 12, 55, 120, 126;
1, 13, 66, 165, 210, 126;
MAPLE
seq(seq( binomial(n-k+1, k-1), k=1..floor((n-2)/2)), n=4..20); # G. C. Greubel, Nov 27 2019
MATHEMATICA
Table[Binomial[n-k+1, k-1], {n, 4, 20}, {k, Floor[(n-2)/2]}]//Flatten
PROG
(PARI) T(n, k) = binomial(n-k+1, k-1);
for(n=4, 20, for(k=1, (n-2)\2, print1(T(n, k), ", "))) \\ G. C. Greubel, Nov 27 2019
(Magma) [Binomial(n-k+1, k-1): k in [1..Floor((n-2)/2)], n in [4..20]]; // G. C. Greubel, Nov 27 2019
(Sage) [[binomial(n-k+1, k-1) for k in (1..floor((n-2)/2))] for n in (4..20)] # G. C. Greubel, Nov 27 2019
(GAP) Flat(List([4..20], n-> List([1..Int((n-2)/2)], k-> Binomial(n-k+1, k-1) ))); # G. C. Greubel, Nov 27 2019
CROSSREFS
Sequence in context: A176320 A190185 A331189 * A066805 A326142 A028284
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Dec 07 2010
EXTENSIONS
Edited by N. J. A. Sloane, Dec 09 2010
More terms added by G. C. Greubel, Nov 27 2019
STATUS
approved