A293926 Triangle read by rows, T(n, k) = Pochhammer(n, k) * Stirling2(2*n, k + n) for n >= 0 and 0 <= k <= n.

1, 1, 1, 7, 12, 6, 90, 195, 180, 60, 1701, 4200, 5320, 3360, 840, 42525, 114135, 176400, 157500, 75600, 15120, 1323652, 3764376, 6679134, 7484400, 5155920, 1995840, 332640, 49329280, 146386240, 287567280, 379387008, 332972640, 186666480, 60540480, 8648640

Offset: 0

Author

Peter Luschny, Oct 22 2017

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0]       1
[1]       1,       1
[2]       7,      12,       6
[3]      90,     195,     180,      60
[4]    1701,    4200,    5320,    3360,     840
[5]   42525,  114135,  176400,  157500,   75600,   15120
[6] 1323652, 3764376, 6679134, 7484400, 5155920, 1995840, 332640
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

T(n,0) = Stirling2(2*n,n) = A007820(n), T(n,n) = A000407(n).

Cf. A293617.

Programs

Maple

A293926 := (n, k) -> A293617(n, n, k ):
seq(seq(A293926(n, k), k=0..n), n=0..7);

Mathematica

A293617[m_, n_, k_] := Pochhammer[m, k] StirlingS2[n + m, k + m];
A293926Row[n_] := Table[A293617[n, n, k], {k, 0, n}];
Table[A293926Row[n], {n, 0, 7}] // Flatten

PARI

for(n=0,10, for(k=0,n, print1(if(n==0 && k==0, 1, ((n+k-1)!/(n-1)!)*stirling(2*n, n + k, 2)), ", "))) \\ G. C. Greubel, Nov 19 2017

Formula

T(n, k) = A293617(n, n, k).