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A154633
a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
3
105, 3465, 19305, 62985, 156009, 326025, 606825, 1038345, 1666665, 2544009, 3728745, 5285385, 7284585, 9803145, 12924009, 16736265, 21335145, 26822025, 33304425, 40896009, 49716585, 59892105, 71554665, 84842505, 99900009, 116877705, 135932265, 157226505, 180929385
OFFSET
0,1
COMMENTS
3 divides a(n).
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
FORMULA
Sum_{n>=0} 1/a(n) = (3*Pi - 8)/144.
G.f.: 3*(35 + 980*x + 1010*x^2 + 20*x^3 + 3*x^4)/(1-x)^5.
a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
Sum_{n>=0} (-1)^n/a(n) = 1/18 - Pi/(48*sqrt(2)). - Amiram Eldar, Feb 27 2022
MATHEMATICA
a[n_] := (4*n + 1)*(4*n + 3)*(4*n + 5)*(4*n + 7); Array[a, 40, 0] (* Amiram Eldar, Feb 27 2022 *)
PROG
(PARI) a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7); \\ Michel Marcus, Aug 21 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jaume Oliver Lafont, Jan 13 2009
STATUS
approved