login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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