A001512 a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).
24, 3024, 24024, 93024, 255024, 570024, 1113024, 1974024, 3258024, 5085024, 7590024, 10923024, 15249024, 20748024, 27615024, 36060024, 46308024, 58599024, 73188024, 90345024, 110355024, 133518024, 160149024, 190578024, 225150024, 264225024, 308178024
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4): n in[0..50]] // Vincenzo Librandi, Aug 02 2010
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Mathematica
Table[Times@@(5n+{1,2,3,4}),{n,0,30}] (* Harvey P. Dale, Jul 15 2019 *) -
PARI
a(n)=(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4) \\ Charles R Greathouse IV, Oct 21 2022
Formula
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]
From Amiram Eldar, Sep 20 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(10-22/sqrt(5))*Pi/30.
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)