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 A005716 Coefficient of x^8 in expansion of (1+x+x^2)^n (Formerly M4975) 12
 1, 15, 90, 357, 1107, 2907, 6765, 14355, 28314, 52624, 93093, 157950, 258570, 410346, 633726, 955434, 1409895, 2040885, 2903428, 4065963, 5612805, 7646925, 10293075, 13701285, 18050760, 23554206, 30462615, 39070540, 49721892 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 4..1000 R. K. Guy, Letter to N. J. A. Sloane, 1987 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Eric Weisstein's World of Mathematics, Trinomial Coefficient Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = binomial(n+1, 5)*(n^2+23*n-84)*(n+10)/336, n >= 4. G.f.: (x^4)*(1+6*x-9*x^2+3*x^3)/(1-x)^9 (Numerator polynomial is N3(8, x) from A063420). a(n) = A027907(n, 8), n >= 4 (ninth column of trinomial coefficients). a(n) = A111808(n,8) for n>7. - Reinhard Zumkeller, Aug 17 2005 a(n) = 9*a(n-1) -36*a(n-2) +84*a(n-3) -126*a(n-4) +126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). Vincenzo Librandi, Jun 16 2012 a(n) = binomial(n,4) + 10*binomial(n,5) + 15*binomial(n,6) + 7*binomial(n,7) + binomial(n,8) (see our comment in A026729). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012 a(n) = GegenbauerC(N, -n, -1/2) where N = 8 if 8 GegenbauerC(`if`(8:=PolynomialRing(Integers()); [ Coefficients((1+x+x^2)^n)[9]: n in [4..32] ]; // Bruno Berselli, Jun 17 2012 CROSSREFS Cf. A000574, A005581, A005712, A005714, A005715, A111808. Sequence in context: A151974 A179096 A001297 * A292055 A263628 A263629 Adjacent sequences:  A005713 A005714 A005715 * A005717 A005718 A005719 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Oct 02 2000 STATUS approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)