A248326 Square array read by downward antidiagonals: super Patalan numbers of order 5.

1, 5, 20, 75, 50, 450, 1375, 500, 750, 10500, 27500, 6875, 5625, 13125, 249375, 577500, 110000, 61875, 78750, 249375, 5985000, 12512500, 1925000, 825000, 721875, 1246875, 4987500, 144637500, 277062500, 35750000, 12375000, 8250000, 9796875, 21375000, 103312500, 3512625000, 6233906250, 692656250

Offset: 0

Author

Tom Richardson, Oct 04 2014

Keywords

• nonn
• easy
• tabl

Comments

Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 5, A025750.

Examples

			T(0..4,0..4) is
  1       5       75      1375    27500
  20      50      500     6875    110000
  450     750     5625    61875   825000
  10500   13125   78750   721875  8250000
  249375  249375  1246875 9796875 97968750
		

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

Cf. A068555, A025750, A034688 (first row), A049382 (first column), A248324, A248325, A248328, A248329, A248332.

Programs

PARI

matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*25^(n+k)*binomial(n-1/5,n+k)) \\ Michel Marcus, Oct 09 2014

Formula

T(0,0)=1, T(n,k) = T(n-1,k)*(25*n-5)/(n+k), T(n,k) = T(n,k-1)*(25*k-20)/(n+k).

G.f.: (x/(1-25*x)^(4/5)+y/(1-25*y)^(1/5))/(x+y-25*x*y).

T(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k).