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 A155744 Triangle T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows. 1
 3, 1, 1, 1, 3, 1, 1, 11, 11, 1, 1, 48, 143, 48, 1, 1, 274, 1835, 1835, 274, 1, 1, 1935, 23649, 51075, 23649, 1935, 1, 1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1, 1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1, 1, 1491876, 59942994, 535933124, 1510548249, 1510548249, 535933124, 59942994, 1491876, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k). Sum_{k=0..n} T(n, k) = 2*n! + A342111(n). - G. C. Greubel, Jun 05 2021 EXAMPLE 3;   1,      1;   1,      3,       1;   1,     11,      11,        1;   1,     48,     143,       48,        1;   1,    274,    1835,     1835,      274,        1;   1,   1935,   23649,    51075,    23649,     1935,       1;   1,  15861,  310639,  1195999,  1195999,   310639,   15861,      1;   1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1; MATHEMATICA T[n_, k_] = (-1)^(n-k)*StirlingS1[n, k] + (-1)^k*StirlingS1[n, n-k] + (-1)^n*StirlingS1[n, k]*StirlingS1[n, n-k]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 05 2021 *) PROG (MAGMA) A155744:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) + (-1)^k*StirlingFirst(n, n-k) + (-1)^(n-k)*StirlingFirst(n, k) >; [A155744(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 05 2021 (Sage) def A155744(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k) + stirling_number1(n, k) + stirling_number1(n, n-k) flatten([[A155744(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 05 2021 CROSSREFS Cf. A000142, A001263, A048994, A342111. Sequence in context: A226203 A327791 A051997 * A086869 A095345 A342671 Adjacent sequences:  A155741 A155742 A155743 * A155745 A155746 A155747 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Jan 26 2009 EXTENSIONS Edited by G. C. Greubel, Jun 05 2021 STATUS approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)