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a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).
2

%I #29 Oct 21 2022 21:11:20

%S 24,3024,24024,93024,255024,570024,1113024,1974024,3258024,5085024,

%T 7590024,10923024,15249024,20748024,27615024,36060024,46308024,

%U 58599024,73188024,90345024,110355024,133518024,160149024,190578024,225150024,264225024,308178024

%N a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).

%H T. D. Noe, <a href="/A001512/b001512.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.: 24*( x^4 + 121*x^3 + 381*x^2 + 121*x + 1 )/( 1-x )^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009 [corrected by _Jaume Oliver Lafont_, Sep 19 2009]

%F From _Amiram Eldar_, Sep 20 2022: (Start)

%F Sum_{n>=0} 1/a(n) = sqrt(10-22/sqrt(5))*Pi/30.

%F Sum_{n>=0} (-1)^n/a(n) = 4*log(2)/15 - 2*log(phi)/(3*sqrt(5)), where phi is the golden ratio (A001622). (End)

%t Table[Times@@(5n+{1,2,3,4}),{n,0,30}] (* _Harvey P. Dale_, Jul 15 2019 *)

%o (Magma) [(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4): n in[0..50]] // _Vincenzo Librandi_, Aug 02 2010

%o (PARI) a(n)=(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4) \\ _Charles R Greathouse IV_, Oct 21 2022

%Y Cf. A001622, A151989.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_