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 A304797 Expansion of x * (d/dx) Sum_{k>=0} k!*x^(k*(k+1)/2)/Product_{j=1..k} (1 - x^j). 1
 0, 1, 2, 9, 12, 25, 66, 91, 152, 243, 570, 715, 1212, 1729, 2702, 5265, 6960, 10489, 15318, 22363, 31100, 57771, 72534, 109411, 151032, 219025, 293930, 421281, 680820, 883369, 1256010, 1727971, 2396000, 3235419, 4447506, 5894875, 9266580, 11691001, 16380470, 21774753 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sum of all parts of all compositions (ordered partitions) of n into distinct parts. LINKS FORMULA a(n) = n*A032020(n). MAPLE b:= proc(n, k) option remember; `if`(k<0 or n<0, 0,      `if`(k=0, `if`(n=0, 1, 0), b(n-k, k) +k*b(n-k, k-1)))     end: a:= n-> n*add(b(n, k), k=0..floor((sqrt(8*n+1)-1)/2)): seq(a(n), n=0..50);  # Alois P. Heinz, May 18 2018 MATHEMATICA nmax = 39; CoefficientList[Series[x D[Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], x], {x, 0, nmax}], x] CROSSREFS Cf. A001787, A032020, A066186, A066189, A097910, A303664. Sequence in context: A053900 A318681 A183207 * A178312 A253608 A126977 Adjacent sequences:  A304794 A304795 A304796 * A304798 A304799 A304800 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 18 2018 STATUS approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)