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 A000920 Differences of 0: 6!*Stirling2(n,6). (Formerly M5473 N2370) 10
 0, 0, 0, 0, 0, 720, 15120, 191520, 1905120, 16435440, 129230640, 953029440, 6711344640, 45674188560, 302899156560, 1969147121760, 12604139926560, 79694820748080, 499018753280880, 3100376804676480, 19141689213218880, 117579844328562000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Number of surjections from an n-element set onto a six-element set, with n >= 6. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007 Number of rows of n colors using exactly six colors.  For n=6, the 720 rows are the 720 permutations of ABCDEF. - Robert A. Russell, Sep 25 2018 REFERENCES H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 212. J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 33. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54. A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911, p. 31. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 P. A. Piza, Kummer numbers, Mathematics Magazine, 21 (1947/1948), 257-260. P. A. Piza, Kummer numbers, Mathematics Magazine, 21 (1947/1948), 257-260. [Annotated scanned copy] A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911. A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911. [Annotated scans of pages 30-33 only] Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720). FORMULA a(n) = Sum((-1)^i*binomial(6, i)*(6-i)^n, i = 0 .. 5). a(n) = 6^n-C(6,5)*5^n+C(6,4)*4^n-C(6,3)*3^n+C(6,2)*2^n-C(6,1) with n>=6. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007 G.f.: 720*x^6/((x-1)*(6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009; checked and corrected by R. J. Mathar, Sep 16 2009] a(n) = 720*A000770(n). - R. J. Mathar, Apr 30 2015 E.g.f.: (exp(x) - 1)^6. - Geoffrey Critzer, May 17 2015 MAPLE 720/(-1+z)/(6*z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); with (combstruct):ZL:=[S, {S=Sequence(U, card=r), U=Set(Z, card>=1)}, labeled]: seq(count(subs(r=6, ZL), size=m), m=1..22); # Zerinvary Lajos, Mar 09 2007 MATHEMATICA CoefficientList[Series[(720*x^5)/((x-1)*(6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 11 2012 *) k=6; Table[k!StirlingS2[n, k], {n, 1, 30}] (* Robert A. Russell, Sep 25 2018 *) PROG (MAGMA) [6^n-Binomial(6, 5)*5^n+Binomial(6, 4)*4^n-Binomial(6, 3)*3^n+Binomial(6, 2)*2^n-Binomial(6, 1): n in [1..30]]; // Vincenzo Librandi, May 18 2015 (PARI) a(n) = 6!*stirling(n, 6, 2); \\ Altug Alkan, Sep 25 2018 CROSSREFS Cf. A001117, A001118, A000918, A000919, A000770. Column 6 of A019538. Sequence in context: A112002 A004033 A056271 * A052779 A254079 A037212 Adjacent sequences:  A000917 A000918 A000919 * A000921 A000922 A000923 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 22 18:48 EST 2019. Contains 319365 sequences. (Running on oeis4.)