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.

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A127740 Natural number transform of Aitken's triangle.

Original entry on oeis.org

1, 2, 4, 6, 9, 15, 20, 28, 40, 60, 75, 100, 135, 185, 260, 312, 402, 522, 684, 906, 1218, 1421, 1785, 2254, 2863, 3661, 4718, 6139, 7016, 8640, 10680, 13256, 16528, 20712, 26104, 33120, 37260, 45153, 54873, 66888, 81801, 100395, 123696, 153063, 190323
Offset: 0

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Author

Gary W. Adamson, Jan 27 2007

Keywords

Comments

Left column (1, 2, 6, 20, ...) = A052889.
Row sums give A127741.

Examples

			First few rows of the triangle:
   1;
   2,   4;
   6,   9,  15;
  20,  28,  40,  60;
  75, 100, 135, 185, 260;
  ...

Crossrefs

Cf. A005493, A052889, A011971, A127741.

Formula

A127648 * A011971 as infinite lower triangular matrices.

A226855 a(n) = n*B(n-1) + n*(n-1)*B(n-2), where the B(i) are Bell numbers (A000110).

Original entry on oeis.org

0, 1, 4, 12, 44, 175, 762, 3605, 18384, 100404, 584070, 3601895, 23451540, 160633681, 1153896772, 8668821600, 67943174000, 554327140739, 4698491153454, 41299244789989, 375844030441560
Offset: 0

Views

Author

Michel Marcus, Jun 19 2013

Keywords

Links

Crossrefs

Cf. A052889 (see Prop 3.1 (ii) in Chern et al. link).

Programs

  • Magma
    [0,1] cat [n*Bell(n-1)+n*(n-1)*Bell(n-2): n in [2..25]]; // Vincenzo Librandi, Jul 16 2013
  • Mathematica
    Table[n BellB[n-1] + n (n-1) BellB[n-2], {n, 0, 30}] (* Vincenzo Librandi, Jul 16 2013 *)
  • PARI
    B(n) = if (n<=1, return (1), return (sum(i=0, n-1, binomial(n-1, i)*B(n-1-i))))
a(n) = n*B(n-1) + n*(n-1)*B(n-2)
Previous Showing 11-12 of 12 results.

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

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