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 A139626 a(n) = binomial(n+4, 4)*6^n. 4
 1, 30, 540, 7560, 90720, 979776, 9797760, 92378880, 831409920, 7205552640, 60526642176, 495217981440, 3961743851520, 31084451758080, 239794342133760, 1822437000216576, 13668277501624320, 101306056776744960, 742911083029463040, 5395880497792942080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n=5) of 7 objects t, u, v, w, z, x, y with repetition allowed, containing exactly four (4) u's. Example: a(1)=30 because we have uuuut, uuutu, uutuu, utuuu, tuuuu, uuuuv, uuuvu, uuvuu, uvuuu, vuuuu, uuuuw, uuuwu, uuwuu, uwuuu, wuuuu, uuuuz, uuuzu, uuzuu, uzuuu, zuuuu, uuuux, uuuxu, uuxuu, uxuuu, xuuuu, uuuuy, uuuyu, uuyuu, uyuuu, yuuuu. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (30,-360,2160,-6480,7776). FORMULA a(n) = A000332(n+4) * A000400(n). - Michel Marcus, Sep 11 2013 G.f.: 1 / (1-6*x)^5. - Colin Barker, Sep 25 2013 From Amiram Eldar, Aug 28 2022: (Start) Sum_{n>=0} 1/a(n) = 548 - 3000*log(6/5). Sum_{n>=0} (-1)^n/a(n) = 8232*log(7/6) - 1268. (End) MAPLE seq(binomial(n+4, 4)*6^n, n=0..22); PROG (Magma) [6^n* Binomial(n+4, 4): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011 (PARI) a(n)=binomial(n+4, 4)*6^n \\ Charles R Greathouse IV, Sep 11 2013 CROSSREFS Cf. A000332, A000400. Sequence in context: A004327 A270499 A286975 * A037961 A143399 A293103 Adjacent sequences: A139623 A139624 A139625 * A139627 A139628 A139629 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jun 12 2008 EXTENSIONS More terms from Colin Barker, Sep 25 2013 STATUS approved

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Last modified August 13 19:33 EDT 2024. Contains 375144 sequences. (Running on oeis4.)