A248329 Square array read by antidiagonals downwards: super Patalan numbers of order 7.

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

Offset: 0

Author

Tom Richardson, Oct 04 2014

Keywords

• nonn
• tabl
• easy

Comments

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

Examples

			T(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
		

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

Programs

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

Formula

T(0,0)=1, T(n,k) = T(n-1,k)*(49*n-7)/(n+k), T(n,k) = T(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).

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