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A174544 A mirrored symmetrical triangle of the Stirling numbers of the second kind. 0

%I

%S 1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,15,15,1,1,1,1,31,90,31,1,1,1,1,63,

%T 301,301,63,1,1,1,1,127,966,1701,966,127,1,1,1,1,255,3025,7770,7770,

%U 3025,255,1,1,1,1,511,9330,34105,42525,34105,9330,511,1,1

%N A mirrored symmetrical triangle of the Stirling numbers of the second kind.

%C Row Sums are: 1, 2, 3, 4, 11, 34, 156, 732, 3891, 22104, 130421,...

%F T(n,0) = 1. T(n,k) = A008277(n,k) if 1<=k<=n/2. T(n,k) = T(n,n-k).

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 1, 1;

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

%e 1, 1, 15, 15, 1, 1;

%e 1, 1, 31, 90, 31, 1, 1;

%e 1, 1, 63, 301, 301, 63, 1, 1;

%e 1, 1, 127, 966, 1701, 966, 127, 1, 1;

%e 1, 1, 255, 3025, 7770, 7770, 3025, 255, 1, 1;

%e 1, 1, 511, 9330, 34105, 42525, 34105, 9330, 511, 1, 1;

%t t[n_, m_, q_] = If[m == 0 || m == n, 1, If[Floor[n/2] >= m, StirlingS2[n, m]*q^ m, StirlingS2[n, n - m]*q^(n - m)]];

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

%K nonn,tabl

%O 0,13

%A _Roger L. Bagula_, Mar 22 2010

%E Formula and NAME cleaned up by _R. J. Mathar_, Aug 28 2013

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Last modified September 20 04:16 EDT 2021. Contains 347577 sequences. (Running on oeis4.)