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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
OFFSET
0,1
COMMENTS
Row sums are: {2, 2, 4, 10, 30, 104, 406, 1754, 8280, 42294, 231950, ...}.
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
(SageMath) [[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 * A383153 A351089 A133831
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 16 2009
STATUS
approved