A208657 Triangular array read by rows: n*binomial(n,n-k+1)-binomial(n-1,n-k) with k = 1..n, n >= 1.

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

Offset

1,3

Comments

Mirror of A208656.

Links

Table of n, a(n) for n=1..59.

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

Crossrefs

Cf. A002061 (second column), A208656, A208658 (row sums), A257055.

Sequence in context: A357939 A188656 A210204 * A329940 A074680 A123496

Adjacent sequences: A208654 A208655 A208656 * A208658 A208659 A208660

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Mar 01 2012

Status

approved