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 A140405 a(n) = binomial(n+6, 6)*5^n. 2
 1, 35, 700, 10500, 131250, 1443750, 14437500, 134062500, 1173046875, 9775390625, 78203125000, 604296875000, 4532226562500, 33120117187500, 236572265625000, 1656005859375000, 11385040283203125, 77016448974609375, 513442993164062500, 3377914428710937500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n>=6) of 6 objects: 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)=35 because we have 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 Table of n, a(n) for n=0..19. Index entries for linear recurrences with constant coefficients, signature (35,-525,4375,-21875,65625,-109375,78125). FORMULA G.f.: 1/(1-5*x)^7. - Zerinvary Lajos, Aug 06 2008 From Amiram Eldar, Aug 29 2022: (Start) Sum_{n>=0} 1/a(n) = 6856 - 30720*log(5/4). Sum_{n>=0} (-1)^n/a(n) = 233280*log(6/5) - 42531. (End) MAPLE seq(binomial(n+6, 6)*5^n, n=0..18); MATHEMATICA Table[Binomial[n+6, 6]5^n, {n, 0, 20}] (* Harvey P. Dale, Dec 03 2017 *) CROSSREFS Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140406. Sequence in context: A202127 A175774 A112504 * A367250 A278361 A145603 Adjacent sequences: A140402 A140403 A140404 * A140406 A140407 A140408 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jun 16 2008 STATUS approved

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Last modified June 25 15:24 EDT 2024. Contains 373705 sequences. (Running on oeis4.)