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 A152918 Triangle read by rows based on the Stirling numbers S1: t(n,m)=Sum[(-1)^(n + 1)* StirlingS1[n, j]*(k + 1 - j)^(n - 1), {j, 0, k + 1}]. 0
 1, 2, 5, 6, 37, 80, 24, 334, 1179, 2644, 120, 3566, 20617, 63413, 146394, 720, 44316, 413608, 1766365, 5161687, 12157088, 5040, 632052, 9362908, 55669771, 207499100, 590541383, 1411732608, 40320, 10212336, 236604140, 1953603356, 9326112285 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Row sums are: {1, 7, 123, 4181, 234110, 19543784, 2275442862, 352293774104, 69988577590464,...}. The sum algorithm is based on the Eulerian number sum with Stirling first kind substituted for the binomial. LINKS Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4. FORMULA t(n,m)=Sum[(-1)^(n + 1)* StirlingS1[n, j]*(k + 1 - j)^(n - 1), {j, 0, k + 1}]. EXAMPLE {1}, {2, 5}, {6, 37, 80}, {24, 334, 1179, 2644}, {120, 3566, 20617, 63413, 146394}, {720, 44316, 413608, 1766365, 5161687, 12157088}, {5040, 632052, 9362908, 55669771, 207499100, 590541383, 1411732608}, {40320, 10212336, 236604140, 1953603356, 9326112285, 32221533668, 90256527071, 218289140928}, {362880, 184767984, 6618132828, 75520418032, 462351260321, 1945272980967, 6403986114493, 17752922644079, 43341720908880} MATHEMATICA Clear[t, n, k]; t[n_, k_] = Sum[(-1)^(n + 1)* StirlingS1[n, j]*(k + 1 - j)^(n - 1), {j, 0, k + 1}]; Table[Table[t[n, k], {k, 1, n - 1}], {n, 2, 10}]; Flatten[%] CROSSREFS Sequence in context: A056441 A164805 A275285 * A276845 A055877 A288799 Adjacent sequences:  A152915 A152916 A152917 * A152919 A152920 A152921 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 15 2008 STATUS approved

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)