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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.
0
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
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
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jun 06 2021
STATUS
approved