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%I #13 Sep 08 2022 08:44:51
%S 1,24,945,6160,21945,57456,124729,238680,417105,680680,1052961,
%T 1560384,2232265,3100800,4201065,5571016,7251489,9286200,11721745,
%U 14607600,17996121,21942544,26504985,31744440
%N a(n) = (2*n-1)*(3*n-1)*(4*n-1)*(5*n-1).
%H G. C. Greubel, <a href="/A033590/b033590.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: (1 + 19*x + 835*x^2 + 1665*x^3 + 360*x^4)/(1-x)^5. - _R. J. Mathar_, Feb 06 2017
%F From _G. C. Greubel_, Mar 05 2020: (Start)
%F a(n) = n^4 * Pochhammer(2 - 1/n, 4) = Product_{j=2..5} (j*n-1).
%F E.g.f.: (1 + 23*x + 449*x^2 + 566*x^3 + 120*x^4)*exp(x). (End)
%p seq( mul(j*n-1, j=2..5), n=0..40); # _G. C. Greubel_, Mar 05 2020
%t Table[(2*n-1)*(3*n-1)*(4*n-1)*(5*n-1), {n,0,40}] (* _G. C. Greubel_, Mar 05 2020 *)
%o (PARI) vector(41, n, my(m=n-1); prod(j=2,5, j*m-1) ) \\ _G. C. Greubel_, Mar 05 2020
%o (Magma) [(2*n-1)*(3*n-1)*(4*n-1)*(5*n-1): n in [0..40]]; // _G. C. Greubel_, Mar 05 2020
%o (Sage) [product(j*n-1 for j in (2..5)) for n in (0..40)] # _G. C. Greubel_, Mar 05 2020
%Y Cf. A060747, A033568, A033589.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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