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%I #19 Sep 08 2022 08:45:47
%S 251,232,243,224,475,2376,9107,26368,63099,132200,251251,443232,
%T 737243,1169224,1782675,2629376,3770107,5275368,7226099,9714400,
%U 12844251,16732232,21508243,27316224,34314875,42678376,52597107,64278368,77947099
%N a(n) = (n+1)*(6*n^4 - 51*n^3 + 161*n^2 - 251*n + 251).
%C The sequence is the numerators of the fifth column of the array on page 56 of the reference. The denominators are A091137(4)=720.
%C The sequence is the binomial transform of the quasi-finite 251, -19, 30, -60, 360, 720, 0, 0, 0, 0, ...
%C The fifth differences are (constant) 720; the fourth differences are 720*n + 360.
%D P. Curtz, Integration numerique des systemes differentiels a conditions initiales, C.C.S.A., Arcueil, 1969.
%H Vincenzo Librandi, <a href="/A165281/b165281.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) mod 10 = A010879(n+1).
%F a(n+1) - a(n) = A157411(n).
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F G.f.: ( 251 - 1274*x + 2616*x^2 - 2774*x^3 + 1901*x^4 ) / (x-1)^6. - _R. J. Mathar_, Jul 06 2011
%t Table[(n+1)(6n^4-51n^3+161n^2-251n+251),{n,0,30}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{251,232,243,224,475,2376},30] (* _Harvey P. Dale_, Aug 20 2014 *)
%o (Magma) [(n+1)*(6*n^4-51*n^3+161*n^2-251*n+251): n in [0..30]]; // _Vincenzo Librandi_, Aug 07 2011
%Y Cf. A157371, A152064.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Sep 13 2009
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