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A174378 Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 4, read by rows.

%I A174378 #6 Nov 29 2021 01:04:52
%S A174378 1,1,1,1,8,1,1,12,12,1,1,16,192,16,1,1,20,320,320,20,1,1,24,480,7680,
%T A174378 480,24,1,1,28,672,13440,13440,672,28,1,1,32,896,21504,430080,21504,
%U A174378 896,32,1,1,36,1152,32256,774144,774144,32256,1152,36,1,1,40,1440,46080,1290240,30965760,1290240,46080,1440,40,1
%N A174378 Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 4, read by rows.
%C A174378 Row sums are: {1, 2, 10, 26, 226, 682, 8690, 28282, 474946, 1615178, ...}.
%H A174378 G. C. Greubel, <a href="/A174378/b174378.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A174378 T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 2.
%F A174378 T(n, n-k) = T(n, k).
%F A174378 T(2*n, n) = A052734(n+1). - _G. C. Greubel_, Nov 28 2021
%e A174378 Triangle begins as:
%e A174378   1;
%e A174378   1,  1;
%e A174378   1,  8,    1;
%e A174378   1, 12,   12,     1;
%e A174378   1, 16,  192,    16,       1;
%e A174378   1, 20,  320,   320,      20,        1;
%e A174378   1, 24,  480,  7680,     480,       24,       1;
%e A174378   1, 28,  672, 13440,   13440,      672,      28,     1;
%e A174378   1, 32,  896, 21504,  430080,    21504,     896,    32,    1;
%e A174378   1, 36, 1152, 32256,  774144,   774144,   32256,  1152,   36,  1;
%e A174378   1, 40, 1440, 46080, 1290240, 30965760, 1290240, 46080, 1440, 40,  1;
%t A174378 T[n_, k_, q_]:= If[Floor[n/2]>=k, n!*q^k/(n-k)!, n!*q^(n-k)/k!];
%t A174378 Table[T[n, k, 4], {n,0,12}, {k,0,n}]//Flatten
%o A174378 (Sage)
%o A174378 f=factorial
%o A174378 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)
%o A174378 flatten([[T(n,k,4) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Nov 28 2021
%Y A174378 Cf. A159623 (q=1), A174376 (q=2), A174377 (q=3), this sequence (q=4).
%Y A174378 Cf. A052734.
%K A174378 nonn,tabl,easy
%O A174378 0,5
%A A174378 _Roger L. Bagula_, Mar 17 2010
%E A174378 Edited by _G. C. Greubel_, Nov 28 2021