A001505 a(n) = (4n+1)(4n+2)(4n+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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• L. B. W. Jolley, Summation of Series, Dover, 1961
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A015219.

Programs

Magma

[(4*n+1)*(4*n+2)*(4*n+3): n in [0..100]]; // Vincenzo Librandi, Apr 04 2011

Mathematica

Table[(4n+1)(4n+2)(4n+3),{n,0,49}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

PARI

a(n)=(4*n+1)*(4*n+2)*(4*n+3) \\ Charles R Greathouse IV, Jun 17 2017

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

E.g.f.: 2*exp(x)*(3 + 102*x + 144*x^2 + 32*x^3). - Stefano Spezia, Aug 24 2025