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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 (list; graph; refs; listen; history; text; internal format)
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 A110217

Adjacent sequences:  A344911 A344912 A344914 * A344916 A344917 A344918

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, Jun 06 2021

STATUS

approved

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Last modified July 26 10:21 EDT 2021. Contains 346294 sequences. (Running on oeis4.)