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

Author

Peter Luschny, Jun 06 2021

Keywords

• nonn
• tabf

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.

Crossrefs

A336614 (row sums).

Cf. A344914.

Programs

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);