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 A142472 Triangle T(n, k) = binomial(n, k) * Sum_{j=k..n} StirlingS1(n, j)*StirlingS1(j, k), read by rows. 1
 1, -4, 1, 21, -18, 1, -140, 240, -48, 1, 1140, -3150, 1300, -100, 1, -11004, 43620, -29700, 4800, -180, 1, 123074, -650769, 647780, -175175, 13965, -294, 1, -1566928, 10517108, -14190400, 5676160, -764400, 34496, -448, 1, 22390488, -184052520, 319680732, -175091112, 35160048, -2698920, 75600, -648, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are: 1, -3, 4, 53, -809, 7537, -41418, -294411, 15463669, -352665269, .... LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened FORMULA T(n, k) = binomial(n, k) * Sum_{j=k..n} StirlingS1(n, j)*StirlingS1(j, k). EXAMPLE The triangle begins as: 1; -4, 1; 21, -18, 1; -140, 240, -48, 1; 1140, -3150, 1300, -100, 1; -11004, 43620, -29700, 4800, -180, 1; 123074, -650769, 647780, -175175, 13965, -294, 1; -1566928, 10517108, -14190400, 5676160, -764400, 34496, -448, 1; 22390488, -184052520, 319680732, -175091112, 35160048, -2698920, 75600, -648, 1; MAPLE A142472:= (n, k)-> binomial(n, k)*add(Stirling1(n, j)*Stirling1(j, k), j=k..n); seq(seq(A142472(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 02 2021 MATHEMATICA T[n_, k_]:= Binomial[n, k]*Sum[StirlingS1[n, j]*StirlingS1[j, k], {j, k, n}]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 02 2021 *) PROG (Magma) A142472:= func< n, k | Binomial(n, k)*(&+[StirlingFirst(n, j)*StirlingFirst(j, k): j in [k..n]]) >; [A142472(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 02 2021 (Sage) def A142472(n, k): return (-1)^(n-k)*binomial(n, k)*sum( stirling_number1(n, j)*stirling_number1(j, k) for j in (k..n) ) flatten([[A142472(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 02 2021 CROSSREFS Cf. A008275, A039814. Sequence in context: A126457 A159841 A202550 * A360089 A299445 A135049 Adjacent sequences: A142469 A142470 A142471 * A142473 A142474 A142475 KEYWORD sign,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 22 2008 EXTENSIONS Edited by N. J. A. Sloane, Sep 26 2008 STATUS approved

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Last modified February 7 12:00 EST 2023. Contains 360115 sequences. (Running on oeis4.)