

A208657


Triangular array read by rows: n*binomial(n,nk+1)binomial(n1,nk) with k = 1..n, n >= 1.


4



0, 1, 3, 2, 7, 8, 3, 13, 21, 15, 4, 21, 44, 46, 24, 5, 31, 80, 110, 85, 35, 6, 43, 132, 225, 230, 141, 48, 7, 57, 203, 413, 525, 427, 217, 63, 8, 73, 296, 700, 1064, 1078, 728, 316, 80, 9, 91, 414, 1116, 1974, 2394, 2016, 1164, 441, 99, 10, 111, 560, 1695
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OFFSET

1,3


COMMENTS



LINKS



EXAMPLE

Triangle begins:
0,
1, 3,
2, 7, 8,
3, 13, 21, 15,
4, 21, 44, 46, 24,
5, 31, 80, 110, 85, 35,
6, 43, 132, 225, 230, 141, 48,
7, 57, 203, 413, 525, 427, 217, 63,
8, 73, 296, 700, 1064, 1078, 728, 316, 80,
9, 91, 414, 1116, 1974, 2394, 2016, 1164, 441, 99;
...


MATHEMATICA

z = 12;
f[n_, k_] := n*Binomial[n, k]  Binomial[n  1, k  1]
t = Table[f[n, k], {n, 1, z}, {k, 1, n}];
TableForm[t] (* A208656 as a triangle *)
Flatten[t] (* A208656 as a sequence *)
r = Table[f[n, k], {n, 1, z}, {k, n, 1, 1}];
TableForm[r] (* A208657 as a triangle *)
Flatten[r] (* A208657 as a sequence *)
Table[Sum[f[n, k], {k, 1, n}], {n, 1, 3 z}](* A208658 *)


PROG

(Magma) [n*Binomial(n, nk+1)Binomial(n1, nk): k in [1..n], n in [1..11]]; // Bruno Berselli, Apr 15 2015


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



