A248328 Square array read by antidiagonals downwards: super Patalan numbers of order 6.
1, 6, 30, 126, 90, 990, 3276, 1260, 1980, 33660, 93366, 24570, 20790, 50490, 1161270, 2800980, 560196, 324324, 424116, 1393524, 40412196, 86830380, 14004900, 6162156, 5513508, 9754668, 40412196, 1414426860, 2753763480, 372130200, 132046200, 89791416, 108694872, 242473176, 1212365880
Offset: 0
Examples
T(0..4,0..4) is 1 6 126 3276 93366 30 90 1260 24570 560196 990 1980 20790 324324 6162156 33660 50490 424116 5513508 89791416 1161270 1393524 9754668 108694872 1548901926
Links
- Thomas M. Richardson, The Super Patalan Numbers, arXiv:1410.5880 [math.CO], 2014.
- Thomas M. Richardson, The Super Patalan Numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3.
Crossrefs
Programs
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PARI
matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*36^(n+k)*binomial(n-1/6,n+k)) \\ Michel Marcus, Oct 09 2014
Formula
T(0,0)=1, T(n,k) = T(n-1,k)*(36*n-6)/(n+k), T(n,k) = T(n,k-1)*(36*k-30)/(n+k).
G.f.: (x/(1-36*x)^(5/6)+y/(1-36*y)^(1/6))/(x+y-36*x*y).
T(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k).
Comments