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 A248326 Square array read by antidiagonals downward: super Patalan numbers of order 5. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 5, A025750. 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. FORMULA a(0,0)=1, a(n,k) = a(n-1,k)*(25*n-5)/(n+k), a(n,k) = a(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). a(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k). EXAMPLE a(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 PROG (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 CROSSREFS Cf. A068555, A025750, A034688 (first row), A049382 (first column), A248324, A248325, A248328, A248329, A248332. Sequence in context: A094806 A289596 A026639 * A022633 A092490 A094828 Adjacent sequences:  A248323 A248324 A248325 * A248327 A248328 A248329 KEYWORD nonn,easy,tabl AUTHOR Tom Richardson, Oct 04 2014 STATUS approved

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Last modified July 6 14:10 EDT 2022. Contains 355110 sequences. (Running on oeis4.)