OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (1/4)*(n+1)*(n+2)*(n+5)*(n+6).
a(n) = A034856(n+2)^2 - 1. - J. M. Bergot, Dec 14 2010
G.f.: 3*(5-4*x+x^2)/(1-x)^5. - Colin Barker, Sep 21 2012
a(n) = Sum_{i=1..n+1} i*(i+2)*(i+4). - Bruno Berselli, Apr 28 2014
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 43/450.
Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/15 - 154/225. (End)
From G. C. Greubel, Mar 05 2025: (Start)
E.g.f.: (1/4)*(60 + 192*x + 114*x^2 + 20*x^3 + x^4)*exp(x). (End)
EXAMPLE
a(0) = C(0+2,2)*C(0+6,2) = C(2,2)*C(6,2) = 1*15 = 155.
a(6) = 1*3*5 + 2*4*6 + 3*5*7 + 4*6*8 + 5*7*9 + 6*8*10 + 7*9*11 = 1848.
MATHEMATICA
f[n_] := Binomial[n + 2, 2] Binomial[n + 6, 2]; Table[f[n], {n, 0, 40}] (* Robert G. Wilson v, Apr 20 2005 *)
CoefficientList[Series[3 (5-4*x+x^2)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 28 2014 *)
PROG
(PARI) a(n)=binomial(n+2, 2)*binomial(n+6, 2) \\ Charles R Greathouse IV, Jun 07 2013
(Magma) [Binomial(n+2, 2)*Binomial(n+6, 2): n in [0..50]]; // Vincenzo Librandi, Apr 28 2014
(SageMath)
def A104473(n): return binomial(n+2, 2)*binomial(n+6, 2)
print([A104473(n) for n in range(51)]) # G. C. Greubel, Mar 05 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Apr 18 2005
STATUS
approved