

A157870


a(n) = (4n+1)(4n+2) = (4n+2)!/(4n)!.


2



2, 30, 90, 182, 306, 462, 650, 870, 1122, 1406, 1722, 2070, 2450, 2862, 3306, 3782, 4290, 4830, 5402, 6006, 6642, 7310, 8010, 8742, 9506, 10302, 11130, 11990, 12882, 13806, 14762, 15750, 16770, 17822, 18906, 20022, 21170, 22350, 23562, 24806, 26082, 27390, 28730, 30102, 31506, 32942
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OFFSET

0,1


COMMENTS

I was trying to prove the irrationality of pi and I encountered this sequence.
A014634 * 2 = A157870. A157870 / 2 = A014634.  Vladimir Joseph Stephan Orlovsky, Mar 10 2009


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = A002378(4n+1) = 2*A014634(n).  R. J. Mathar, Mar 11 2009
G.f.: 2*(1+12*x+3*x^2)/(1x)^3.  Vincenzo Librandi, Jul 10 2012
a(n) = 3*a(n1) 3 *a(n2) + a(n3).  Vincenzo Librandi, Jul 10 2012


MATHEMATICA

lst={}; Do[a=(2*n+1)*(4*n+1)*2; AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)
Table[(4n+1)*(4n+2), {n, 0, 50}] (* Vincenzo Librandi, Jul 10 2012 *)


PROG

(MAGMA) (4*n+1)*(4*n+2). // Vincenzo Librandi Jul 10 2012
(PARI) a(n)=(4*n+1)*(4*n+2) \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Sequence in context: A189100 A085637 A193177 * A285991 A078838 A267851
Adjacent sequences: A157867 A157868 A157869 * A157871 A157872 A157873


KEYWORD

nonn,easy


AUTHOR

SUNKU Sai Swaroop (sai2020(AT)gmail.com), Mar 08 2009


EXTENSIONS

Definition corrected and sequence extended by R. J. Mathar, Mar 11 2009


STATUS

approved



