A244492 - OEIS

%I #23 Jul 16 2022 11:49:11

%S 1,0,3,3,0,6,0,15,0,10,15,0,45,0,15,0,105,0,105,0,21,105,0,420,0,210,

%T 0,28,0,945,0,1260,0,378,0,36,945,0,4725,0,3150,0,630,0,45

%N Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = n!/(2^i*i!*k!), where k=n-2i (or 0 for entries with wrong parity).

%H J. East and R. D. Gray, <a href="http://arxiv.org/abs/1404.2359">Idempotent generators in finite partition monoids and related semigroups</a>, arXiv preprint arXiv:1404.2359 [math.GR], 2014-2016.

%e Triangle begins:

%e     1;

%e     0,   3;

%e     3,   0,    6;

%e     0,  15,    0,   10;

%e    15,   0,   45,    0,   15;

%e     0, 105,    0,  105,    0,  21;

%e   105,   0,  420,    0,  210,   0,  28;

%e     0, 945,    0, 1260,    0, 378,   0, 36;

%e   945,   0, 4725,    0, 3150,   0, 630,  0, 45;

%e   ...

%t T[n_, k_] := With[{i = (n-k)/2}, If[EvenQ[n-k], n!/(2^i i! k!), 0]];

%t Table[T[n, k], {n, 2, 10}, {k, 0, n-2}] // Flatten (* _Jean-François Alcover_, Nov 25 2018 *)

%Y This is A099174 without the two rightmost diagonals.

%K nonn,tabl

%O 0,3

%A _N. J. A. Sloane_, Jul 05 2014