A174377 Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 3, read by rows.

1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 12, 108, 12, 1, 1, 15, 180, 180, 15, 1, 1, 18, 270, 3240, 270, 18, 1, 1, 21, 378, 5670, 5670, 378, 21, 1, 1, 24, 504, 9072, 136080, 9072, 504, 24, 1, 1, 27, 648, 13608, 244944, 244944, 13608, 648, 27, 1, 1, 30, 810, 19440, 408240, 7348320, 408240, 19440, 810, 30, 1

Offset: 0

Author

Roger L. Bagula, Mar 17 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are: {1, 2, 8, 20, 134, 392, 3818, 12140, 155282, 518456, 8205362, ...}.

Examples

			Triangle begins as:
  1;
  1,  1;
  1,  6,   1;
  1,  9,   9,     1;
  1, 12, 108,    12,      1;
  1, 15, 180,   180,     15,       1;
  1, 18, 270,  3240,    270,      18,      1;
  1, 21, 378,  5670,   5670,     378,     21,     1;
  1, 24, 504,  9072, 136080,    9072,    504,    24,   1;
  1, 27, 648, 13608, 244944,  244944,  13608,   648,  27,  1;
  1, 30, 810, 19440, 408240, 7348320, 408240, 19440, 810, 30,  1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A159623 (q=1), A174376 (q=2), this sequence (q=3), A174378 (q=4).

Cf. A221954.

Programs

Mathematica

T[n_, k_, q_]:= If[Floor[n/2]>=k, n!*q^k/(n-k)!, n!*q^(n-k)/k!];
Table[T[n, k, 3], {n,0,12}, {k,0,n}]//Flatten

Sage

f=factorial
def T(n,k,q): return f(n)*q^k/f(n-k) if ((n//2)>k-1) else f(n)*q^(n-k)/f(k)
flatten([[T(n,k,3) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 28 2021

Formula

T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 3.

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

T(2*n, n) = A221954(n+1). - G. C. Greubel, Nov 28 2021

Extensions

Edited by G. C. Greubel, Nov 28 2021