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A008493
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Expansion of (1-x^11) / (1-x)^11.
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2
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1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756, 352715, 646635, 1144000, 1960970, 3267759, 5308732, 8428277, 13103662, 19986252, 29952637, 44167409, 64159524, 91914394, 129984074, 181618140, 250918096, 343018401, 464297471, 622622286
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OFFSET
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0,2
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COMMENTS
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Coordination sequence for 10-dimensional cyclotomic lattice Z[zeta_11].
Growth series of the affine Weyl group of type A10. - Paul E. Gunnells, Jan 06 2017
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REFERENCES
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R. Bott, The geometry and the representation theory of compact Lie groups, in: Representation Theory of Lie Groups, in: London Math. Soc. Lecture Note Ser., vol. 34, Cambridge University Press, Cambridge, 1979, pp. 65-90.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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a(n) = 11*n*(193248 + 152900*n^2 + 16401*n^4 + 330*n^6 + n^8)/362880 for n>0. - Colin Barker, Jan 06 2017
E.g.f.: 1 + x*(3991680 + 7983360*x + 7318080*x^2 + 3160080*x^3 + 765072*x^4 + 105336*x^5 + 8712*x^6 + 396*x^7 + 11*x^8)*exp(x)/362880. - G. C. Greubel, Nov 07 2019
a(n) = 10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Wesley Ivan Hurt, Jun 07 2021
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MAPLE
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1, seq(11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880, n=1..40); # G. C. Greubel, Nov 07 2019
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MATHEMATICA
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Table[If[n==0, 1, 11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880], {n, 0, 40}] (* G. C. Greubel, Nov 07 2019 *)
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PROG
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(PARI) Vec((1-x^11)/(1-x)^11 + O(x^40)) \\ Colin Barker, Jan 06 2017
(Magma) [1] cat [11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880: n in [1..40]]; // G. C. Greubel, Nov 07 2019
(Sage) [1]+[11*n*(193248+152900*n^2+16401*n^4+330*n^6+n^8)/362880 for n in (1..40)] # G. C. Greubel, Nov 07 2019
(GAP) Concatenation([1], List([1..40], n-> 11*n*(193248+152900*n^2 +16401*n^4 +330*n^6+n^8)/362880 )); # G. C. Greubel, Nov 07 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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