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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

%I

%S 1,2,4,8,2,16,16,32,80,64,320,40,128,1120,560,256,3584,4480,512,10752,

%T 26880,2240,1024,30720,134400,44800,2048,84480,591360,492800,4096,

%U 225280,2365440,3942400,246400,8192,585728,8785920,25625600,6406400

%N 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.

%H mjqxxxx, <a href="https://math.stackexchange.com/q/4164050">Proof of conjectured formulas for A336614</a>, Mathematics Stack Exchange.

%e [ 0] 1;

%e [ 1] 2;

%e [ 2] 4;

%e [ 3] 8, 2;

%e [ 4] 16, 16;

%e [ 5] 32, 80;

%e [ 6] 64, 320, 40;

%e [ 7] 128, 1120, 560;

%e [ 8] 256, 3584, 4480;

%e [ 9] 512, 10752, 26880, 2240;

%e [10] 1024, 30720, 134400, 44800;

%e [11] 2048, 84480, 591360, 492800;

%e [12] 4096, 225280, 2365440, 3942400, 246400.

%p t := (n, k) -> k^n*n!: s := (n, k) -> 2^(3*k)*(n - 3*k)!:

%p T := (n, k) -> t(n, 2) / (t(k, 3) * s(n, k)):

%p seq(lprint([n], seq(T(n, k), k = 0..n/3)), n = 0..12);

%Y A336614 (row sums).

%Y Cf. A344914.

%K nonn,tabf

%O 0,2

%A _Peter Luschny_, Jun 06 2021

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Last modified September 23 20:31 EDT 2021. Contains 347617 sequences. (Running on oeis4.)