OFFSET
0,2
COMMENTS
Convolution of the sequences (0,3,5,0,0,0,...) and (binomial(n+3, 3)), n >= 0. - Emeric Deutsch, Aug 30 2007
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = A132121(n,2) for n > 1.
G.f.: x*(3+5*x)/(1-x)^4. - Emeric Deutsch, Aug 30 2007
From Bruno Berselli, Nov 25 2010: (Start)
Sum_{n>=1} 1/a(n) = 54 - 24*(sqrt(2)+1)*Pi/7 - 24*(sqrt(2)+8)*log(2)/7 + 48*sqrt(2)*log(2-sqrt(2))/7. - Amiram Eldar, May 20 2023
E.g.f.: exp(x)*x*(18 + 33*x + 8*x^2)/6. - Stefano Spezia, Feb 21 2024
MAPLE
seq((1/6)*n*(n+1)*(8*n+1), n=0..40); # Emeric Deutsch, Aug 30 2007
MATHEMATICA
a[n_] := n*(n + 1)*(8*n + 1)/6; Array[a, 42, 0] (* Amiram Eldar, May 20 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 12 2007
STATUS
approved