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

0,2

Links

Table of n, a(n) for n=0..39.

mjqxxxx, Proof of conjectured formulas for A336614, Mathematics Stack Exchange.

Example

[ 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.

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);

Crossrefs

A336614 (row sums).

Cf. A344914.

Sequence in context: A064897 A167203 A263410 * A285334 A086317 A356693

Adjacent sequences: A344912 A344913 A344914 * A344916 A344917 A344918

Keyword

nonn,tabf

Author

Peter Luschny, Jun 06 2021

Status

approved