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A142472 Triangle read by rows: t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}]. 0

%I

%S 1,-4,1,21,-18,1,-140,240,-48,1,1140,-3150,1300,-100,1,-11004,43620,

%T -29700,4800,-180,1,123074,-650769,647780,-175175,13965,-294,1,

%U -1566928,10517108,-14190400,5676160,-764400,34496,-448,1,22390488,-184052520,319680732,-175091112,35160048,-2698920,75600

%N Triangle read by rows: t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}].

%C Row sums are: {1, -3, 4, 53, -809, 7537, -41418, -294411, 15463669, -352665269, ...}.

%F t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}].

%e {1},

%e {-4, 1},

%e {21, -18, 1},

%e {-140, 240, -48, 1},

%e {1140, -3150, 1300, -100, 1},

%e {-11004, 43620, -29700, 4800, -180, 1},

%e {123074, -650769,647780, -175175, 13965, -294, 1},

%e {-1566928, 10517108, -14190400, 5676160, -764400, 34496, -448, 1},

%e {22390488, -184052520, 319680732, -175091112, 35160048, -2698920, 75600, -648, 1},

%e {-354995760, 3478726080, -7492500000, 5330088750, -1475938800, 169943760, -8139600, 151200, -900, 1}

%t t[n_, m_] = Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]

%Y Cf. A039814.

%K sign,tabl

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 22 2008

%E Edited by _N. J. A. Sloane_, Sep 26 2008

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)