A107873 Triangle, read by rows, where T(n,k) = binomial(n*(n-1)/2 - k*(k-1)/2 + n-k+3, n-k).
1, 4, 1, 15, 5, 1, 84, 28, 6, 1, 715, 220, 45, 7, 1, 8568, 2380, 455, 66, 8, 1, 134596, 33649, 5985, 816, 91, 9, 1, 2629575, 593775, 98280, 12650, 1330, 120, 10, 1, 61523748, 12620256, 1947792, 237336, 23751, 2024, 153, 11, 1, 1677106640, 314457495, 45379620, 5245786, 501942, 40920, 2925, 190, 12, 1
Offset: 0
Examples
Triangle begins:
1;
4, 1;
15, 5, 1;
84, 28, 6, 1;
715, 220, 45, 7, 1;
8568, 2380, 455, 66, 8, 1;
134596, 33649, 5985, 816, 91, 9, 1;
2629575, 593775, 98280, 12650, 1330, 120, 10, 1; ...
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..5000
Programs
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Magma
[Binomial(3+Floor((n-k)*(n+k+1)/2), n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 19 2022
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Mathematica
Flatten[Table[Binomial[(n(n-1))/2-(k(k-1))/2+n-k+3,n-k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Oct 03 2015 *) -
PARI
T(n,k)=binomial(n*(n-1)/2-k*(k-1)/2 +n-k+3,n-k)
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Sage
flatten([[binomial(3+(n-k)*(n+k+1)/2, n-k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 19 2022
Formula
From G. C. Greubel, Feb 19 2022: (Start)
T(n,k) = binomial(n*(n-1)/2 - k*(k-1)/2 + n-k+3, n-k).
T(n, 0) = A107874(n).
T(n, 1) = A107875(n). (End)
Comments