A248326 Square array read by antidiagonals downward: 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

0,2

Comments

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

Links

Table of n, a(n) for n=0..37.

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