A344915 T(n, k) = (3^(-k)*n!*2^(n - 3*k))/(k!*(n - 3*k)!), for n >= 0 and 0 <= k <= floor(n/3). Triangle read by rows.
1, 2, 4, 8, 2, 16, 16, 32, 80, 64, 320, 40, 128, 1120, 560, 256, 3584, 4480, 512, 10752, 26880, 2240, 1024, 30720, 134400, 44800, 2048, 84480, 591360, 492800, 4096, 225280, 2365440, 3942400, 246400, 8192, 585728, 8785920, 25625600, 6406400
Offset: 0
Examples
[ 0] 1; [ 1] 2; [ 2] 4; [ 3] 8, 2; [ 4] 16, 16; [ 5] 32, 80; [ 6] 64, 320, 40; [ 7] 128, 1120, 560; [ 8] 256, 3584, 4480; [ 9] 512, 10752, 26880, 2240; [10] 1024, 30720, 134400, 44800; [11] 2048, 84480, 591360, 492800; [12] 4096, 225280, 2365440, 3942400, 246400.
Links
- mjqxxxx, Proof of conjectured formulas for A336614, Mathematics Stack Exchange.
Programs
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Maple
t := (n, k) -> k^n*n!: s := (n, k) -> 2^(3*k)*(n - 3*k)!: T := (n, k) -> t(n, 2) / (t(k, 3) * s(n, k)): seq(lprint([n], seq(T(n, k), k = 0..n/3)), n = 0..12);