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<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55, -1320, 18150, -157773, 902055, -3416930, 8409500, -12753576, 10628640, -3628800).
INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=370">Encyclopedia of Combinatorial Structures 370</a>.
<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).
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(Python)
def A001557(n): return sum(i**n for i in range(1, 11)) # Chai Wah Wu, Oct 24 2024
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a(n) = 1^n + 2^n + ... + 10^n.
a(n) = sum(j^n,Sum_{j=1..10), } j^n, n >= 0.
E.g.f.: exp(x) + exp(2*x) + exp(3*x) + exp(4*x) + exp(5*x) + exp(6*x) + exp(7*x) + exp(8*x) + exp(9*x) + exp(10*x). - Vladeta Jovovic, May 08 2002
O.g.f.: (2 - 11*x) *(5 - 220*x + 4070*x^2 - 41140*x^3 + 247049*x^4 - 896368*x^5 + 1903836*x^6 - 2143152*x^7 + 966240*x^8)/product((1-j*x),Product_{j=1..10} (1 - j*x).
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M. Abramowitz and I. A. Stegun, eds., <a href="http://appswww.nrbookconvertit.com/abramowitz_and_stegunGo/ConvertIt/Reference/indexAMS55.htmlASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].