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

0,2

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: A266387 A008526 A057425 * A073376 A094429 A246434

Adjacent sequences: A248326 A248327 A248328 * A248330 A248331 A248332

Keyword

nonn,tabl,easy

Author

Tom Richardson, Oct 04 2014

Status

approved