cp's OEIS Frontend

A228887 a(n) = binomial(3*n + 1,3).

%I A228887 #45 Sep 21 2024 02:30:32
%S A228887 4,35,120,286,560,969,1540,2300,3276,4495,5984,7770,9880,12341,15180,
%T A228887 18424,22100,26235,30856,35990,41664,47905,54740,62196,70300,79079,
%U A228887 88560,98770,109736,121485,134044,147440,161700,176851,192920,209934,227920,246905
%N A228887 a(n) = binomial(3*n + 1,3).
%H A228887 Vincenzo Librandi, <a href="/A228887/b228887.txt">Table of n, a(n) for n = 1..1000</a>
%H A228887 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A228887 a(n) = -a(-n) = binomial(3*n + 1,3) = 1/6*(3*n + 1)*(3*n)*(3*n - 1).
%F A228887 G.f.: x*(4 + 19*x + 4*x^2)/(1 - x)^4 = 4*x + 35*x^2 + 120*x^3 + ....
%F A228887 Sum_{n>=1} 1/a(n) = 3*log(3) - 3.
%F A228887 Sum_{n>=1} (-1)^n/a(n) = 4*log(2) - 3.
%F A228887 E.g.f.: exp(x)*x*(8 + 27*x + 9*x^2)/2. - _Stefano Spezia_, Sep 20 2024
%p A228887 seq(binomial(3*n+1,3), n = 1..38);
%t A228887 Table[(Binomial[3n + 1, 3]), {n, 40}] (* _Vincenzo Librandi_, Sep 10 2013 *)
%t A228887 LinearRecurrence[{4,-6,4,-1},{4,35,120,286},40] (* _Harvey P. Dale_, Jan 11 2015 *)
%o A228887 (Magma) [Binomial(3*n+1,3): n in [1..40]]; // _Vincenzo Librandi_, Sep 10 2013
%Y A228887 Cf. A006566 (binomial(3*n,3)) and A228888 (binomial(3*n + 2,3)).
%K A228887 nonn,easy
%O A228887 1,1
%A A228887 _Peter Bala_, Sep 09 2013