login
A001505
a(n) = (4n+1)(4n+2)(4n+3).
3
6, 210, 990, 2730, 5814, 10626, 17550, 26970, 39270, 54834, 74046, 97290, 124950, 157410, 195054, 238266, 287430, 342930, 405150, 474474, 551286, 635970, 728910, 830490, 941094, 1061106, 1190910, 1330890, 1481430, 1642914, 1815726, 2000250, 2196870, 2405970
OFFSET
0,1
FORMULA
a(n) = 6 * A015219(n).
Sum_{n>=0} 1/a(n) = log(2)/4 = 0.17328679513998... [Jolley eq. 253. Typo fixed by Jaume Oliver Lafont, Jan 09 2009]
G.f.: 6*(1+x)*(x^2+30*x+1) / (x-1)^4. - R. J. Mathar, Apr 02 2011
Sum_{n>=0} (-1)^n/a(n) = (sqrt(2)-1)*Pi/8. - Amiram Eldar, Sep 17 2022
MATHEMATICA
Table[(4n+1)(4n+2)(4n+3), {n, 0, 49}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
PROG
(Magma) [(4*n+1)*(4*n+2)*(4*n+3): n in [0..100]]; // Vincenzo Librandi, Apr 04 2011
(PARI) a(n)=(4*n+1)*(4*n+2)*(4*n+3) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A015219.
Sequence in context: A094805 A055193 A346015 * A327248 A084694 A285149
KEYWORD
nonn,easy
STATUS
approved