A154844 Triangle T(n, k) = S(n, k) + S(n, n-k), where S are the Stirling numbers (A048993) of the second kind, read by rows.

2, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 14, 7, 1, 1, 11, 40, 40, 11, 1, 1, 16, 96, 180, 96, 16, 1, 1, 22, 203, 651, 651, 203, 22, 1, 1, 29, 393, 2016, 3402, 2016, 393, 29, 1, 1, 37, 717, 5671, 14721, 14721, 5671, 717, 37, 1, 1, 46, 1261, 15210, 56932, 85050, 56932, 15210, 1261, 46, 1

Offset

0,1

Comments

Row sums are: {2, 2, 4, 10, 30, 104, 406, 1754, 8280, 42294, 231950, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n, m) = S(n, m) + S(n, n-m), where S(n,k) = A048993(n,k).

Sum_{k=0..n} T(n,k) = 2*A000110(n). - Philippe Deléham, Feb 17 2013

Example

Triangle begins as:
  2;
  1,  1;
  1,  2,    1;
  1,  4,    4,     1;
  1,  7,   14,     7,     1;
  1, 11,   40,    40,    11,     1;
  1, 16,   96,   180,    96,    16,     1;
  1, 22,  203,   651,   651,   203,    22,     1;
  1, 29,  393,  2016,  3402,  2016,   393,    29,    1;
  1, 37,  717,  5671, 14721, 14721,  5671,   717,   37,  1;
  1, 46, 1261, 15210, 56932, 85050, 56932, 15210, 1261, 46, 1;

Mathematica

Table[StirlingS2[n, m] + StirlingS2[n, n-m], {n, 0, 10}, {m, 0, n}]//Flatten

Prog

(PARI) {T(n, m) = stirling(n, k, 2) + stirling(n, n-m, 2)}; \\ G. C. Greubel, May 01 2019
(Magma) [[StirlingSecond(n, k) + StirlingSecond(n, n-k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 01 2019
(Sage) [[stirling_number2(n, k) + stirling_number2(n, n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, May 01 2019

Crossrefs

Cf. A048993.

Sequence in context: A155798 A055652 A290084 * A351089 A133831 A325613

Adjacent sequences: A154841 A154842 A154843 * A154845 A154846 A154847

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 16 2009

Status

approved