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%I #17 Feb 27 2022 05:46:17
%S 105,3465,19305,62985,156009,326025,606825,1038345,1666665,2544009,
%T 3728745,5285385,7284585,9803145,12924009,16736265,21335145,26822025,
%U 33304425,40896009,49716585,59892105,71554665,84842505,99900009,116877705,135932265,157226505,180929385
%N a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
%C 3 divides a(n).
%C For n=5k, 5k+1, 5k+2 and 5k+3, a(n) is a multiple of 5. For n=5k+4, a(n)-9 is a multiple of 100. - _Michel Marcus_, Aug 21 2013
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F Sum_{n>=0} 1/a(n) = (3*Pi - 8)/144.
%F G.f.: 3*(35 + 980*x + 1010*x^2 + 20*x^3 + 3*x^4)/(1-x)^5.
%F a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F Sum_{n>=0} (-1)^n/a(n) = 1/18 - Pi/(48*sqrt(2)). - _Amiram Eldar_, Feb 27 2022
%t a[n_] := (4*n + 1)*(4*n + 3)*(4*n + 5)*(4*n + 7); Array[a, 40, 0] (* _Amiram Eldar_, Feb 27 2022 *)
%o (PARI) a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7); \\ _Michel Marcus_, Aug 21 2013
%Y Cf. A133766, A001539, A157142.
%K easy,nonn
%O 0,1
%A _Jaume Oliver Lafont_, Jan 13 2009
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