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 A059372 Revert transform of factorials n! (n >= 1). 3
 1, -2, 2, -4, -4, -48, -336, -2928, -28144, -298528, -3454432, -43286528, -583835648, -8433987584, -129941213184, -2127349165824, -36889047574272, -675548628690432, -13030733384956416, -264111424634864640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First diagonal of triangle in A059370. REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 171, #34. LINKS T. D. Noe and Vaclav Kotesovec, Table of n, a(n) for n = 1..400 (first 100 terms from T. D. Noe) M. H. Albert, M. D. Atkinson and M. Klazar, The Enumeration of Simple Permutations, J. Integer Seqs., Vol. 6, 2003. E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, arXiv:math/0407326 [math.CO], 2004; J. Num. Theory 117 (2006), 191-215. FORMULA a(n) ~ -exp(-2) * n! * (1 - 4/n + 2/n^2 - 34/(3*n^3) - 296/(3*n^4) - 4818/(5*n^5) - 508532/(45*n^6)). - Vaclav Kotesovec, Aug 04 2015 G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} k! * A(x)^k. - Ilya Gutkovskiy, Apr 22 2020 MAPLE # From Transforms, see the footer of the page. REVERT([seq(k!, k=1..20)]); # Peter Luschny, May 01 2021 MATHEMATICA nmax = 20; t[n_, k_] := t[n, k] = Sum[(m + 1)!*t[n - m - 1, k - 1], {m, 0, n - k}]; t[n_, 1] = n!; t[n_, n_] = 1; tnk = Table[t[n, k], {n, 1, nmax}, {k, 1, nmax}]; Inverse[tnk][[All, 1]] (* Jean-François Alcover, Jul 13 2016 *) CROSSREFS Cf. A000142, A059370. Sequence in context: A025557 A285909 A322253 * A161422 A049261 A135018 Adjacent sequences:  A059369 A059370 A059371 * A059373 A059374 A059375 KEYWORD sign,easy AUTHOR N. J. A. Sloane, Jan 28 2001 EXTENSIONS More terms from Vladeta Jovovic, Mar 05 2001 Definition refined by Georg Fischer, May 01 2021 STATUS approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)