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.

A119829 Diagonal sum of number triangle A119828.

Original entry on oeis.org

1, 2, 25, 732, 40681, 3648990, 480817681, 87417943256, 20966398997041, 6412838733766170, 2436104066933508841, 1125217445576328664692, 621010503476937955204825, 403601732164215102065708342
Offset: 0

Views

Author

Paul Barry, May 25 2006

Keywords

Programs

  • Mathematica
    Table[Sum[(2(n-k))!/(2k)!,{k,0,Floor[n/2]}],{n,0,20}] (* Harvey P. Dale, Aug 26 2024 *)

Formula

a(n)=sum{k=0..floor(n/2), (2(n-k))!/(2k)!}

A119830 Bi-diagonal inverse of (2n)!/(2k)!.

Original entry on oeis.org

1, -2, 1, 0, -12, 1, 0, 0, -30, 1, 0, 0, 0, -56, 1, 0, 0, 0, 0, -90, 1, 0, 0, 0, 0, 0, -132, 1, 0, 0, 0, 0, 0, 0, -182, 1, 0, 0, 0, 0, 0, 0, 0, -240, 1, 0, 0, 0, 0, 0, 0, 0, 0, -306, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -462, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 1, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Paul Barry, May 25 2006

Keywords

Comments

Row sums are 1-2n(n-1)=1-b(n). Inverse of A119828.

Examples

			Triangle begins
1,
-2, 1,
0, -12, 1,
0, 0, -30, 1,
0, 0, 0, -56, 1,
0, 0, 0, 0, -90, 1,
0, 0, 0, 0, 0, -132, 1,
0, 0, 0, 0, 0, 0, -182, 1,
0, 0, 0, 0, 0, 0, 0, -240, 1,
0, 0, 0, 0, 0, 0, 0, 0, -306, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -462, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -650, 1

Formula

Column k has g.f. x^k(1-b(k+1)x) where b(n)=2n(2n-1).

A119831 Number triangle (3n)!/(3k)!.

Original entry on oeis.org

1, 6, 1, 720, 120, 1, 362880, 60480, 504, 1, 479001600, 79833600, 665280, 1320, 1, 1307674368000, 217945728000, 1816214400, 3603600, 2730, 1, 6402373705728000, 1067062284288000, 8892185702400, 17643225600, 13366080, 4896, 1
Offset: 0

Views

Author

Paul Barry, May 25 2006

Keywords

Comments

Row sums are A087350. Inverse is bi-diagonal array A119832.

Examples

			Triangle begins
1,
6, 1,
720, 120, 1,
362880, 60480, 504, 1,
479001600, 79833600, 665280, 1320, 1,
1307674368000, 217945728000, 1816214400, 3603600, 2730, 1

Crossrefs

Cf. A119828.

Programs

  • Mathematica
    Flatten[Table[(3n)!/(3k)!,{n,0,10},{k,0,n}]] (* Harvey P. Dale, Jan 19 2013 *)

Formula

Number triangle T(n,k)=[k<=n]*(3n)!/(3k)!
Showing 1-3 of 3 results.

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

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