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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A133831 A325613 A305054

Adjacent sequences:  A154841 A154842 A154843 * A154845 A154846 A154847

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Jan 16 2009

STATUS

approved

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Last modified January 23 16:44 EST 2020. Contains 331172 sequences. (Running on oeis4.)