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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

%I #18 Sep 08 2022 08:45:40

%S 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,

%T 22,203,651,651,203,22,1,1,29,393,2016,3402,2016,393,29,1,1,37,717,

%U 5671,14721,14721,5671,717,37,1,1,46,1261,15210,56932,85050,56932,15210,1261,46,1

%N 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.

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

%H G. C. Greubel, <a href="/A154844/b154844.txt">Rows n = 0..100 of triangle, flattened</a>

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

%F Sum_{k=0..n} T(n,k) = 2*A000110(n). - _Philippe Deléham_, Feb 17 2013

%e Triangle begins as:

%e 2;

%e 1, 1;

%e 1, 2, 1;

%e 1, 4, 4, 1;

%e 1, 7, 14, 7, 1;

%e 1, 11, 40, 40, 11, 1;

%e 1, 16, 96, 180, 96, 16, 1;

%e 1, 22, 203, 651, 651, 203, 22, 1;

%e 1, 29, 393, 2016, 3402, 2016, 393, 29, 1;

%e 1, 37, 717, 5671, 14721, 14721, 5671, 717, 37, 1;

%e 1, 46, 1261, 15210, 56932, 85050, 56932, 15210, 1261, 46, 1;

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

%o (PARI) {T(n,m) = stirling(n,k,2) + stirling(n,n-m,2)}; \\ _G. C. Greubel_, May 01 2019

%o (Magma) [[StirlingSecond(n,k) + StirlingSecond(n,n-k): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, May 01 2019

%o (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

%Y Cf. A048993.

%K nonn,tabl

%O 0,1

%A _Roger L. Bagula_, Jan 16 2009

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)