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%I #13 Jan 03 2024 06:48:32
%S 0,0,2,48,304,999,2393,4791,8542,14039,21719,32063,45596,62887,84549,
%T 111239,143658,182551,228707,282959,346184,419303,503281,599127,
%U 707894,830679,968623,1122911,1294772,1485479,1696349,1928743,2184066,2463767
%N a(n) = (n-1)*(n-2)^4 - A028294(n), for n > 4, with a(1) = a(2) = 0, a(3) = 2, and a(4) = 48.
%H G. C. Greubel, <a href="/A075690/b075690.txt">Table of n, a(n) for n = 1..1000</a>
%H Ed Pegg Jr., <a href="http://www.mathpuzzle.com/pancakes.htm">Pancakes</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _G. C. Greubel_, Jan 03 2024: (Start)
%F a(n) = (n-1)*(n-2)^4 - A028294(n) + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
%F a(n) = (11*n^4 + 19*n^3 - 632*n^2 + 2012*n - 1686)/6 + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].
%F G.f.: x^3*(2 + 38*x + 84*x^2 - 61*x^3 - 32*x^4 + 14*x^5 - x^6)/(1-x)^5.
%F E.g.f.: (1/6)*(-1686 + 1410*x - 498*x^2 + 85*x^3 + 11*x^4)*exp(x) + 281 + 46*x - 23*x^2/2 - 9*x^3/3! + x^4/4!. (End)
%t LinearRecurrence[{5,-10,10,-5,1}, {0,0,2,48,304,999,2393,4791,8542}, 50] (* _G. C. Greubel_, Jan 03 2024 *)
%o (Magma) [0,0,2,48] cat [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6: n in [4..50]]; // _G. C. Greubel_, Jan 03 2024
%o (SageMath) [0,0,2,48] + [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6 for n in range(4,51)] # _G. C. Greubel_, Jan 03 2024
%Y Cf. A028294.
%K nonn
%O 1,3
%A _Jon Perry_, Oct 12 2002
%E More terms from _David Wasserman_, Jan 22 2005
%E Name clarified by _G. C. Greubel_, Jan 03 2024
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