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 A173246 Expansion of (1+x)^50 * (1-x)/(1 - x^51). 1
 1, 49, 1175, 18375, 210700, 1888460, 13771940, 83993700, 436994250, 1968555050, 7766844470, 27081460630, 84045912300, 233460867500, 582985137700, 1312983918820, 2672860120455, 4923689695575, 8206149492625, 12352414499425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From G. C. Greubel, Feb 16 2021: (Start) Let a(n) be the coefficients of the expansion then a(n+51) = a(n) (i.e. periodic length 50) and a(m+26) = - a(25-m) for 0 <= m <= 24. Expansions of the form (1+x)^m * (1-x)/(1 - x^(m+1)) have the coefficients a(n) = Sum_{j=0..(m+1)*n} ( binomial(m, n-(m+1)*j) - binomial(m, n-(m+1)*j-1) ). (End) LINKS G. C. Greubel, Table of n, a(n) for n = 0..509 Index entries for linear recurrences with constant coefficients, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1). FORMULA G.f.: (1+x)^50 / Sum_{j=0..50} x^j. From G. C. Greubel, Feb 16 2021: (Start) G.f.: (1+x)^50 * (1-x)/(1 - x^51). a(n) = (-1)*Sum_{j=1..50} a(n-j) for n > 50. a(n) = Sum_{j=0..51*n} ( binomial(50, n-51*j) - binomial(50, n-51*j-1) ), n > 0. (End) MAPLE m:= 40; S:= series( (1+x)^50*(1-x)/(1-x^51), x, m+1); seq(coeff(S, x, j), j = 0..m); # G. C. Greubel, Feb 16 2021 MATHEMATICA CoefficientList[Series[(1+x)^50*(1-x)/(1-x^51), {x, 0, 40}], x] (* modified by G. C. Greubel, Feb 16 2021 *) PROG (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)^50*(1-x)/(1-x^51) )); // G. C. Greubel, Feb 16 2021 (Sage) def A173246_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( (1+x)^50*(1-x)/(1-x^51) ).list() A173246_list(40) # G. C. Greubel, Feb 16 2021 CROSSREFS Cf. A173245. Sequence in context: A284642 A304046 A264877 * A017765 A163005 A161694 Adjacent sequences: A173243 A173244 A173245 * A173247 A173248 A173249 KEYWORD sign,easy,less AUTHOR Roger L. Bagula, Feb 13 2010 EXTENSIONS Edited by G. C. Greubel, Feb 16 2021 STATUS approved

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Last modified February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)