A342311 T(n, k) = (n - k + 2)*binomial(2*n, n + k - 2). Triangle read by rows, T(n, k) for 0 <= k <= n.

0, 0, 2, 4, 12, 12, 30, 60, 60, 30, 168, 280, 280, 168, 56, 840, 1260, 1260, 840, 360, 90, 3960, 5544, 5544, 3960, 1980, 660, 132, 18018, 24024, 24024, 18018, 10010, 4004, 1092, 182, 80080, 102960, 102960, 80080, 48048, 21840, 7280, 1680, 240

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Example

[0] 0
[1] 0,      2
[2] 4,      12,     12
[3] 30,     60,     60,     30
[4] 168,    280,    280,    168,    56
[5] 840,    1260,   1260,   840,    360,    90
[6] 3960,   5544,   5544,   3960,   1980,   660,    132
[7] 18018,  24024,  24024,  18018,  10010,  4004,   1092,  182
[8] 80080,  102960, 102960, 80080,  48048,  21840,  7280,  1680,  240
[9] 350064, 437580, 437580, 350064, 222768, 111384, 42840, 12240, 2448, 306

Maple

T := (n, k) -> (n - k + 2)*binomial(2*n, n + k - 2):
seq(seq(T(n, k), k=0..n), n=0..9);

Crossrefs

Cf. A002939 (main diagonal), A217213, A002740.

Sequence in context: A168342 A309515 A375551 * A358502 A141668 A087796

Adjacent sequences: A342308 A342309 A342310 * A342312 A342313 A342314

Keyword

nonn,tabl

Author

Peter Luschny, Mar 08 2021

Status

approved