cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A248326 Square array read by downward antidiagonals: super Patalan numbers of order 5.

Original entry on oeis.org

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

Views

Author

Tom Richardson, Oct 04 2014

Keywords

Comments

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

Examples

			T(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

Links

Crossrefs

Cf. A068555, A025750, A034688 (first row), A049382 (first column), A248324, A248325, A248328, A248329, A248332.

Programs

  • 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

Formula

T(0,0)=1, T(n,k) = T(n-1,k)*(25*n-5)/(n+k), T(n,k) = T(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).
T(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k).

A248328 Square array read by antidiagonals downwards: super Patalan numbers of order 6.

Original entry on oeis.org

1, 6, 30, 126, 90, 990, 3276, 1260, 1980, 33660, 93366, 24570, 20790, 50490, 1161270, 2800980, 560196, 324324, 424116, 1393524, 40412196, 86830380, 14004900, 6162156, 5513508, 9754668, 40412196, 1414426860, 2753763480, 372130200, 132046200, 89791416, 108694872, 242473176, 1212365880
Offset: 0

Views

Author

Tom Richardson, Oct 04 2014

Keywords

Comments

Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 6, A025751.

Examples

			T(0..4,0..4) is
  1          6         126       3276      93366
  30         90        1260      24570     560196
  990        1980      20790     324324    6162156
  33660      50490     424116    5513508   89791416
  1161270    1393524   9754668   108694872 1548901926

Links

Crossrefs

Cf. A068555, A025751, A004993 (first row), A004994 (first column), A004995 (second row), A004996 (second column), A248324, A248325, A248326, A248329, A248332.

Programs

  • PARI
    matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*36^(n+k)*binomial(n-1/6,n+k)) \\ Michel Marcus, Oct 09 2014

Formula

T(0,0)=1, T(n,k) = T(n-1,k)*(36*n-6)/(n+k), T(n,k) = T(n,k-1)*(36*k-30)/(n+k).
G.f.: (x/(1-36*x)^(5/6)+y/(1-36*y)^(1/6))/(x+y-36*x*y).
T(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k).

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

Original entry on oeis.org

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

Views

Author

Tom Richardson, Oct 04 2014

Keywords

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

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).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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