A329120 The q-analog T(q; n,k) of the triangle A163626 for 0 <= k <= n, for q=3.

1, 1, -1, 1, -5, 4, 1, -21, 72, -52, 1, -85, 1020, -3016, 2080, 1, -341, 13600, -133900, 372320, -251680, 1, -1365, 178164, -5532800, 50406720, -136662240, 91611520, 1, -5461, 2321592, -223628132, 6320525120, -55844268480, 149876446720, -100131391360

Offset: 0

Author

Werner Schulte, Nov 05 2019

Keywords

• sign
• tabl

Comments

For more information see A308326. There you'll find formulas for the general case depending on some fixed integer q.

Examples

			The triangle T(3; n,k) starts:
n\ k: 0     1      2        3        4          5        6
==========================================================
   0: 1
   1: 1    -1
   2: 1    -5      4
   3: 1   -21     72      -52
   4: 1   -85   1020    -3016     2080
   5: 1  -341  13600  -133900   372320    -251680
   6: 1 -1365 178164 -5532800 50406720 -136662240 91611520
etc.
		

Crossrefs

Cf. A163626, A308326.

Programs

PARI

{ T(n,k) = if( k<0 || k>n, 0, if( k==0, 1, (3^(k+1) - 1)/2 * T(n-1,k) - (3^k - 1)/2 * T(n-1,k-1)))};
for(n=0, 7, for(k=0, n, print1(T(n,k), ", ")))