login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248329 Square array read by antidiagonals downwards: super Patalan numbers of order 7. 3
1, 7, 42, 196, 147, 1911, 6860, 2744, 4459, 89180, 264110, 72030, 62426, 156065, 4213755, 10722866, 2218524, 1310946, 1747928, 5899257, 200574738, 450360372, 75060062, 33647614, 30588740, 55059732, 234003861, 9594158301, 19365495996, 2702162232, 975780806, 672952280, 825895980, 1872030888 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 7, A025752.

LINKS

Table of n, a(n) for n=0..33.

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)*(49*n-7)/(n+k), a(n,k) = a(n,k-1)*(49*k-42)/(n+k).

G.f.: ((x/(1-49*x)^(6/7)+y/(1-49*y)^(1/7))/(x+y-49*x*y).

a(n,k) = (-1)^k*49^(n+k)*binomial(n-1/7,n+k).

EXAMPLE

a(0..4,0..4) is

1           7          196        6860       264110

42          147        2744       72030      2218524

1911        4459       62426      1310946    33647614

89180       156065     1747928    30588740   672952280

4213755     5899257    55059732   825895980  15898497615

PROG

(PARI) matrix(5, 5, nn, kk, n=nn-1; k=kk-1; (-1)^k*49^(n+k)*binomial(n-1/7, n+k)) \\ Michel Marcus, Oct 09 2014

CROSSREFS

Cf. A068555, A025752, A034835 (first row), A216703 (first column), A248324, A248325, A248326, A248328, A248332.

Sequence in context: A212144 A266387 A057425 * A073376 A094429 A246434

Adjacent sequences:  A248326 A248327 A248328 * A248330 A248331 A248332

KEYWORD

nonn,tabl,easy

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 08:11 EST 2020. Contains 331337 sequences. (Running on oeis4.)