A253666
Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.
Original entry on oeis.org
1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 6, 24, 36, 24, 6, 30, 150, 300, 300, 150, 30, 20, 120, 300, 400, 300, 120, 20, 140, 980, 2940, 4900, 4900, 2940, 980, 140, 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70, 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630
Offset: 0
Triangle begins:
. 1;
. 1, 1;
. 2, 4, 2;
. 6, 18, 18, 6;
. 6, 24, 36, 24, 6;
. 30, 150, 300, 300, 150, 30;
. 20, 120, 300, 400, 300, 120, 20;
. 140, 980, 2940, 4900, 4900, 2940, 980, 140;
. 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70;
. 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630; etc.
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[Binomial(n,k)*Factorial(n)/Factorial(Floor(n/2))^2: k in [0..n], n in [0..10]]; // Bruno Berselli, Feb 02 2015
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T := (n,k) -> n!*binomial(n,k)/(iquo(n,2)!)^2:
seq(print(seq(T(n,k), k=0..n)), n=0..9);
A338654
T(n, k) = 2^n * Product_{j=1..k} (j/2)^((-1)^(j - 1)). Triangle read by rows, for 0 <= k <= n.
Original entry on oeis.org
1, 2, 1, 4, 2, 2, 8, 4, 4, 6, 16, 8, 8, 12, 6, 32, 16, 16, 24, 12, 30, 64, 32, 32, 48, 24, 60, 20, 128, 64, 64, 96, 48, 120, 40, 140, 256, 128, 128, 192, 96, 240, 80, 280, 70, 512, 256, 256, 384, 192, 480, 160, 560, 140, 630, 1024, 512, 512, 768, 384, 960, 320, 1120, 280, 1260, 252
Offset: 0
Triangle start:
[0] 1
[1] 2, 1
[2] 4, 2, 2
[3] 8, 4, 4, 6
[4] 16, 8, 8, 12, 6
[5] 32, 16, 16, 24, 12, 30
[6] 64, 32, 32, 48, 24, 60, 20
[7] 128, 64, 64, 96, 48, 120, 40, 140
[8] 256, 128, 128, 192, 96, 240, 80, 280, 70
[9] 512, 256, 256, 384, 192, 480, 160, 560, 140, 630
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T := (n, k) -> 2^n*mul((j/2)^((-1)^(j - 1)), j = 1 .. k):
seq(seq(T(n, k), k=0..n), n=0..9);
# Recurrence:
Trow := proc(n) if n = 0 then return [1] fi; Trow(n - 1);
n^irem(n, 2) * (4/n)^irem(n + 1, 2) * %[n]; [op(2 * %%), %] end:
seq(print(Trow(n)), n = 0..9);
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t(n, k) = 2^n * prod(j=1, k, ((j/2)^((-1)^(j - 1))))
trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print(""))
/* Print upper 10 rows of the triangle as follows: */
trianglerows(10) \\ Felix Fröhlich, Apr 22 2021
Showing 1-2 of 2 results.