A253666 Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.

1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 6, 24, 36, 24, 6, 30, 150, 300, 300, 150, 30, 20, 120, 300, 400, 300, 120, 20, 140, 980, 2940, 4900, 4900, 2940, 980, 140, 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70, 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = C(n,k)*A056040(k).

T(2*n,n) = C(2*n,n)^2.

Example

Triangle begins:
.   1;
.   1,    1;
.   2,    4,     2;
.   6,   18,    18,     6;
.   6,   24,    36,    24,     6;
.  30,  150,   300,   300,   150,    30;
.  20,  120,   300,   400,   300,   120,    20;
. 140,  980,  2940,  4900,  4900,  2940,   980,   140;
.  70,  560,  1960,  3920,  4900,  3920,  1960,   560,   70;
. 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630; etc.

Maple

T := (n, k) -> n!*binomial(n, k)/(iquo(n, 2)!)^2:
seq(print(seq(T(n, k), k=0..n)), n=0..9);

Prog

(Magma) [Binomial(n, k)*Factorial(n)/Factorial(Floor(n/2))^2: k in [0..n], n in [0..10]]; // Bruno Berselli, Feb 02 2015

Crossrefs

Cf. A021012, A196347, A002894.

Row sums are A253665.

Sequence in context: A205839 A138024 A167656 * A174298 A196347 A021012

Adjacent sequences: A253663 A253664 A253665 * A253667 A253668 A253669

Keyword

nonn,tabl

Author

Peter Luschny, Feb 01 2015

Status

approved