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 A189376 Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^2). 4
 1, 3, 6, 10, 17, 27, 40, 56, 78, 106, 140, 180, 230, 290, 360, 440, 535, 645, 770, 910, 1071, 1253, 1456, 1680, 1932, 2212, 2520, 2856, 3228, 3636, 4080, 4560, 5085, 5655, 6270, 6930, 7645, 8415, 9240, 10120, 11066, 12078 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The Gi2 triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of the Gi2 and other triangle sums see A180662. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2,-6,6,-2,-1,3,-3,1). FORMULA a(n) = sum(A144678(n-k), k=0..n). Gi2(n) = A189376(n-1) - A189376(n-2) - A189376(n-5) + 2*A189376(n-6) with A189376(n)=0 for n <= -1. a(0)=1, a(1)=3, a(2)=6, a(3)=10, a(4)=17, a(5)=27, a(6)=40, a(7)=56, a(8)=78, a(9)=106, a(10)=140, a(n)=3*a(n-1)-3*a(n-2)+a(n-3)+ 2*a(n-4)- 6*a(n-5)+6*a(n-6)-2*a(n-7)-a(n-8)+3*a(n-9)-3*a(n-10)+a(n-11). - Harvey P. Dale, Apr 12 2015 MAPLE a:= n-> coeff (series (1/((1-x)^5*(x^3+x^2+x+1)^2), x, n+1), x, n): seq (a(n), n=0..50); MATHEMATICA CoefficientList[Series[1/((1-x)^5(x^3+x^2+x+1)^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 1, 2, -6, 6, -2, -1, 3, -3, 1}, {1, 3, 6, 10, 17, 27, 40, 56, 78, 106, 140}, 50] (* Harvey P. Dale, Apr 12 2015 *) CROSSREFS Cf. A139600, A189374, A189375. Sequence in context: A308699 A286304 A005045 * A069241 A092263 A259968 Adjacent sequences:  A189373 A189374 A189375 * A189377 A189378 A189379 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Apr 29 2011 STATUS approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)