A293926 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

FORMULA

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

EXAMPLE

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

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

PROG

(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

CROSSREFS

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

Cf. A293617.

Sequence in context: A126710 A300729 A152199 * A038598 A180570 A074474

Adjacent sequences: A293923 A293924 A293925 * A293927 A293928 A293929

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 22 2017

STATUS

approved