%I #26 Jan 29 2022 01:18:59

%S 1,1,1,1,10,1,1,35,91,1,1,84,966,820,1,1,165,5082,24970,7381,1,1,286,

%T 18447,273988,631631,66430,1,1,455,53053,1768195,14057043,15857205,

%U 597871,1,1,680,129948,8187608,157280838,704652312,397027996,5380840,1

%N Triangle of central factorial numbers 4^k T(2n+1, 2n+1-2k).

%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

%H Robert James Purser, <a href="https://doi.org/10.25923/d9rn-fd18">Mobius Net Cubed-Sphere Gnomonic Grids</a>, U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service, National Centers for Environmental Protection, 2018.

%F G.f. of i-th right-hand column is x/Product_{j=1..i+1} (1 - (2j-1)^2*x).

%e From _Wesley Transue_, Jan 21 2012: (Start)

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 10, 1;

%e 1, 35, 91, 1;

%e 1, 84, 966, 820, 1;

%e 1, 165, 5082, 24970, 7381, 1;

%e 1, 286, 18447, 273988, 631631, 66430, 1;

%e 1, 455, 53053, 1768195, 14057043, 15857205, 597871, 1;

%e 1, 680, 129948, 8187608, 157280838, 704652312, 397027996, 5380840, 1;

%e (End)

%t Flatten[Table[Sum[(-1)^(q+1) 4^(p-n) (2p+2q-2n-1)^(2n+1)/((2n+1-2p-q)! q!), {q, 0, n-p}], {n, 0, 8}, {p, 0, n}]] (* _Wesley Transue_, Jan 21 2012 *)

%Y Cf. A008955-A008957, A036969.

%Y Columns include A000447. Right-hand columns include A002452, A002453.

%K nonn,tabl,easy,nice

%O 0,5

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Apr 16 2000