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 A176277 Sum over the odd entries of the rows in the triangle Worpitzky(n, k)*Harmonic(k) (A176276). 2
 0, 1, 3, 18, 125, 1020, 9667, 104790, 1281177, 17457840, 262493231, 4318429962, 77178551749, 1489209086820, 30859393432155, 683549418431934, 16118484827641841, 403156528379483160, 10661349675027656839 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..420 Peter Luschny, A sequence transformation and the Bernoulli numbers. FORMULA a(n) = Sum_{k=0..n} (k mod 2) abs(Stirling1(k+1, 2)*Stirling2(n+1, k+1)). EXAMPLE Let W(n, k) be the Worpitzky numbers and H(n) the harmonic numbers. a(3) = W(3,1)H(1) + W(3,3)H(3) = 7*1 + 6*(11/6) = 18. MAPLE A176277 := proc(n) local k; add((k mod 2)*T176276(n, k), k=0..n) end; MATHEMATICA a[1] = 1; a[n_]:= Sum[ StirlingS2[n+1, k+1]*k!*HarmonicNumber[k], {k, 0, n, 2}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 30 2013 *) PROG (PARI) a(n) = if(n<2, n, sum(k=0, n, k!*stirling(n+1, k+1, 2)*sum(j=1, k, 1/j)) ); \\ G. C. Greubel, Nov 24 2019 (MAGMA) [n lt 2 select n else (&+[Abs(StirlingFirst(k+1, 2)*StirlingSecond(n+1, k+1)): k in [0..n]])/2: n in [0..25]]; (Sage) def a(n):     if (n<2): return n     else: return sum( factorial(k)*stirling_number1(n+1, k+1)*harmonic_number(k) for k in (0..n))/2 [a(n) for n in (0..25)] # G. C. Greubel, Nov 24 2019 (GAP) a:= function(n)     if n<2 then return n;     else return Sum([0..n], k-> AbsInt(Stirling1(k+1, 2) * Stirling2(n+1, k+1)))/2;     fi; end; List([0..25], n-> a(n)); # G. C. Greubel, Nov 24 2019 CROSSREFS Cf. A028246, A176276. Sequence in context: A199421 A305869 A181998 * A289429 A004987 A074557 Adjacent sequences:  A176274 A176275 A176276 * A176278 A176279 A176280 KEYWORD easy,nonn AUTHOR Peter Luschny, Apr 14 2010 STATUS approved

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Last modified May 29 10:05 EDT 2020. Contains 334699 sequences. (Running on oeis4.)