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 A198204 Series reversion of (1 - t*x)*log(1 + x) with respect to x. 5
 1, 1, 2, 1, 9, 12, 1, 28, 120, 120, 1, 75, 750, 2100, 1680, 1, 186, 3780, 21840, 45360, 30240, 1, 441, 16856, 176400, 705600, 1164240, 665280, 1, 1016, 69552, 1224720, 8316000, 25280640, 34594560, 17297280, 1, 2295, 272250, 7692300, 82577880, 408648240, 998917920, 1167566400, 518918400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This triangle is A133399 read by diagonals. LINKS FORMULA T(n,k) = k!*binomial(n + k - 1,k)*Stirling2(n,k + 1) (n >= 1, k >=0). E.g.f.: A(x,t) = series reversion of (1 - t*x)*log(1 + x) w.r.t. x = x + (1 + 2*t)*x^2/2! + (1 + 9*t + 12*t^2)*x^3/3! + .... Main diagonal A001813, first subdiagonal A002691. Column 1 A058877, column 2 A133386. Row sums A052892. 1 - t*A(x,t) = x/series reversion of x*(1 - t(exp(x) - 1)) with respect to x. Cf. A141618. - Peter Bala, Oct 22 2015 EXAMPLE Triangle begins .n\k.|..0....1.....2......3......4......5 = = = = = = = = = = = = = = = = = = = = = ..1..|..1 ..2..|..1....2 ..3..|..1....9....12 ..4..|..1...28...120....120 ..5..|..1...75...750...2100...1680 ..6..|..1..186..3780..21840..45360..30240 ... MATHEMATICA Flatten[CoefficientList[CoefficientList[InverseSeries[Series[Log[1 + x]*(1 - t*x), {x, 0, 9}]], x]*Table[n!, {n, 0, 9}], t]] (* Peter Luschny, Oct 25 2015 *) CROSSREFS Cf. A001813, A002691, A052892, A058877, A133386, A133399, A141618. Sequence in context: A063579 A240085 A078623 * A099599 A085488 A072265 Adjacent sequences:  A198201 A198202 A198203 * A198205 A198206 A198207 KEYWORD nonn,easy,tabl AUTHOR Peter Bala, Jul 31 2012 STATUS approved

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Last modified June 1 13:11 EDT 2020. Contains 334762 sequences. (Running on oeis4.)