A157870 a(n) = (4*n+1)*(4*n+2) = (4*n+2)!/(4*n)!.

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

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A002378, A014634, A016813, A016825, A157870.

Programs

Magma

(4*n+1)*(4*n+2); // Vincenzo Librandi Jul 10 2012

Mathematica

Table[(4n+1)*(4n+2),{n,0,50}] (* Vincenzo Librandi, Jul 10 2012 *)

PARI

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

Formula

a(n) = A002378(4*n+1) = 2*A014634(n). - R. J. Mathar, Mar 11 2009

From Vincenzo Librandi, Jul 10 2012: (Start)

G.f.: 2*(1+12*x+3*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

From Amiram Eldar, Mar 01 2022: (Start)

Sum_{n>=0} 1/a(n) = Pi/8 + log(2)/4.

Sum_{n>=0} (-1)^n/a(n) = ((sqrt(2)-1)*Pi + sqrt(2)*log((2+sqrt(2))/(2-sqrt(2))))/8. (End)

From Elmo R. Oliveira, Oct 30 2024: (Start)

E.g.f.: 2*exp(x)*(1 + 14*x + 8*x^2).

a(n) = A016813(n)*A016825(n). (End)

Extensions

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