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 A140520 a(n) = binomial(n+9, 9)*5^n. 1
 1, 50, 1375, 27500, 446875, 6256250, 78203125, 893750000, 9496093750, 94960937500, 902128906250, 8201171875000, 71760253906250, 607202148437500, 4987731933593750, 39901855468750000, 311733245849609375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n>=9) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly nine (9) u's. Example: a(1)=50 because we have uuuuuuuuut, uuuuuuuuuv, uuuuuuuuuz, uuuuuuuuux, uuuuuuuuuy, uuuuuuuutu, uuuuuuuuvu, uuuuuuuuzu, uuuuuuuuxu, uuuuuuuuyu, uuuuuuutuu, uuuuuuuvuu, uuuuuuuzuu, uuuuuuuxuu, uuuuuuuyuu, uuuuuutuuu, uuuuuuvuuu, uuuuuuzuuu, uuuuuuxuuu, uuuuuuyuuu, uuuuutuuuu, uuuuuvuuuu, uuuuuzuuuu, uuuuuxuuuu, uuuuuyuuuu, uuuutuuuuu, uuuuvuuuuu, uuuuzuuuuu, uuuuxuuuuu, uuuuyuuuuu, uuutuuuuuu, uuuvuuuuuu, uuuzuuuuuu, uuuxuuuuuu, uuuyuuuuuu, uutuuuuuuu, uuvuuuuuuu, uuzuuuuuuu, uuxuuuuuuu, uuyuuuuuuu, utuuuuuuuu, uvuuuuuuuu, uzuuuuuuuu, uxuuuuuuuu. uyuuuuuuuu, tuuuuuuuuu, vuuuuuuuuu, zuuuuuuuuu, xuuuuuuuuu. yuuuuuuuuu. LINKS FORMULA From Chai Wah Wu, Mar 20 2017: (Start) a(n) = 50*a(n-1) - 1125*a(n-2) + 15000*a(n-3) - 131250*a(n-4) + 787500*a(n-5) - 3281250*a(n-6) + 9375000*a(n-7) - 17578125*a(n-8) + 19531250*a(n-9) - 9765625*a(n-10) for n > 9. G.f.: 1/(1 - 5*x)^10. (End) MAPLE seq(binomial(n+9, 9)*5^n, n=0..20); MATHEMATICA Table[Binomial[n + 9, 9] 5^n, {n, 0, 16}] (* or *) CoefficientList[Series[1/(1 - 5 x)^10, {x, 0, 16}], x] (* Michael De Vlieger, Mar 20 2017 *) PROG (Sage)[lucas_number2(n, 5, 0)*binomial(n, 9)/5^9 for n in range(9, 26)] # Zerinvary Lajos, Mar 12 2009 CROSSREFS Sequence in context: A283311 A031602 A231743 * A114251 A004351 A229316 Adjacent sequences:  A140517 A140518 A140519 * A140521 A140522 A140523 KEYWORD nonn AUTHOR Zerinvary Lajos, Jul 02 2008 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)