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 A036226 Expansion of 1/(1-7*x)^7. 9
 1, 49, 1372, 28812, 504210, 7764834, 108707676, 1413199788, 17311697403, 201969803035, 2262061793992, 24471395771368, 256949655599364, 2628792630362724, 26287926303627240, 257621677775546952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n >= 6) of 8 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. - Zerinvary Lajos, Jun 16 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (49, -1029, 12005, -84035, 352947, -823543, 823543). FORMULA a(n) = 7^n*binomial(n+6, 6). G.f.: 1/(1-7*x)^7. a(n) = 49*a(n-1) - 1029*a(n-2) + 12005*a(n-3) - 84035*a(n-4) + 352947*a(n-5) - 823543*a(n-6) + 823543*a(n-7), a(0)=1, a(1)=49, a(2)=1372, a(3)=28812, a(4)=504210, a(5)=7764834, a(6)=108707676. - Harvey P. Dale, Feb 21 2013 MAPLE seq(binomial(n+6, 6)*7^n, n=0..16); # Zerinvary Lajos, Jun 16 2008 MATHEMATICA CoefficientList[Series[1/(1-7x)^7, {x, 0, 20}], x] (* or *) LinearRecurrence[ {49, -1029, 12005, -84035, 352947, -823543, 823543}, {1, 49, 1372, 28812, 504210, 7764834, 108707676}, 20] (* Harvey P. Dale, Feb 21 2013 *) PROG (Sage)[lucas_number2(n, 7, 0)*binomial(n, 6)/7^6 for n in range(6, 22)] # Zerinvary Lajos, Mar 13 2009 (MAGMA) [7^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011 CROSSREFS Cf. A036084. Sequence in context: A228258 A282930 A012238 * A032655 A001458 A004374 Adjacent sequences:  A036223 A036224 A036225 * A036227 A036228 A036229 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)