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A174376
Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 2, read by rows.
4
1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 48, 8, 1, 1, 10, 80, 80, 10, 1, 1, 12, 120, 960, 120, 12, 1, 1, 14, 168, 1680, 1680, 168, 14, 1, 1, 16, 224, 2688, 26880, 2688, 224, 16, 1, 1, 18, 288, 4032, 48384, 48384, 4032, 288, 18, 1, 1, 20, 360, 5760, 80640, 967680, 80640, 5760, 360, 20, 1
OFFSET
0,5
COMMENTS
Row sums are: {1, 2, 6, 14, 66, 182, 1226, 3726, 32738, 105446, 1141242, ...}.
FORMULA
T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 2.
T(n, n-k) = T(n, k).
T(2*n, n) = A052714(n+1). - G. C. Greubel, Nov 28 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 4, 1;
1, 6, 6, 1;
1, 8, 48, 8, 1;
1, 10, 80, 80, 10, 1;
1, 12, 120, 960, 120, 12, 1;
1, 14, 168, 1680, 1680, 168, 14, 1;
1, 16, 224, 2688, 26880, 2688, 224, 16, 1;
1, 18, 288, 4032, 48384, 48384, 4032, 288, 18, 1;
1, 20, 360, 5760, 80640, 967680, 80640, 5760, 360, 20, 1;
MATHEMATICA
T[n_, k_, q_]:= If[Floor[n/2]>=k, n!*q^k/(n-k)!, n!*q^(n-k)/k!];
Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(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, 2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 28 2021
CROSSREFS
Cf. A159623 (q=1), this sequence (q=2), A174377 (q=3), A174378 (q=4).
Cf. A052714.
Sequence in context: A102413 A144480 A144463 * A131399 A069322 A208332
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Mar 17 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 28 2021
STATUS
approved