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 A140406 Binomial(n+6,6)*8^n. 7
 1, 56, 1792, 43008, 860160, 15138816, 242221056, 3598712832, 50381979648, 671759728640, 8598524526592, 106309030510592, 1275708366127104, 14915974742409216, 170468282770391040, 1909244767028379648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n>=6) of 9 objects:p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. If n=6 then a(0)= 1 Example: a(1)=56 because we have uuuuuup, uuuuupu, uuuupuu, uuupuuu, uupuuuu, upuuuuu, puuuuuu, uuuuuur, uuuuuru, uuuuruu, uuuruuu, uuruuuu, uruuuuu, ruuuuuu, uuuuuus, uuuuusu, uuuusuu, uuusuuu, uusuuuu, usuuuuu, suuuuuu, uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu, uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu, uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu, uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu, uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 FORMULA G.f.: 1/(1-8*x)^7. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008] a(0)=1, a(1)=56, a(2)=1792, a(3)=43008, a(4)=860160, a(5)=15138816, a(6)=242221056, a(n)=56*a(n-1)-1344*a(n-2)+17920*a(n-3)- 143360*a(n-4)+ 688128*a(n-5)-1835008*a(n-6)+2097152*a(n-7) [From Harvey P. Dale, Dec 15 2011] MAPLE seq(binomial(n+6, 6)*8^n, n=0..17); MATHEMATICA Table[Binomial[n+6, 6]8^n, {n, 0, 20}] (* or *) LinearRecurrence[ {56, -1344, 17920, -143360, 688128, -1835008, 2097152}, {1, 56, 1792, 43008, 860160, 15138816, 242221056}, 20] (* From Harvey P. Dale, Dec 15 2011 *) PROG (MAGMA) [8^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011 (PARI) a(n)=binomial(n+6, 6)<<(3*n) \\ Charles R Greathouse IV, Dec 15 2011 CROSSREFS Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140405. Sequence in context: A035799 A017719 A050989 * A075512 A223958 A000504 Adjacent sequences:  A140403 A140404 A140405 * A140407 A140408 A140409 KEYWORD nonn,easy,changed AUTHOR Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008 STATUS approved

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