cp's OEIS Frontend

A143690 a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, ...].

%I A143690 #22 Aug 14 2025 20:42:19
%S A143690 1,7,27,70,145,261,427,652,945,1315,1771,2322,2977,3745,4635,5656,
%T A143690 6817,8127,9595,11230,13041,15037,17227,19620,22225,25051,28107,31402,
%U A143690 34945,38745,42811,47152,51777,56695,61915,67446,73297,79477,85995,92860,100081,107667
%N A143690 a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, ...].
%C A143690 Binomial transform of [1, 6, 14, 9, 0, 0, 0,...].
%C A143690 Row sums of triangle A033292.
%H A143690 G. C. Greubel, <a href="/A143690/b143690.txt">Table of n, a(n) for n = 0..1000</a>
%H A143690 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A143690 From _R. J. Mathar_, Aug 29 2008: (Start)
%F A143690 G.f.: (1 +3*x +5*x^2)/(1-x)^4.
%F A143690 a(n) = A002412(n+1) + 5*A000292(n-1). (End)
%F A143690 a(n) = A000326(n+1) + (n+1)*A000326(n). - _Bruno Berselli_, Jun 07 2013
%F A143690 From _G. C. Greubel_, May 30 2021: (Start)
%F A143690 a(n) = (n+1)*(3*n^2 +2*n +2)/2.
%F A143690 E.g.f.: (1/2)*(2 +12*x +14*x^2 +3*x^3)*exp(x). (End)
%e A143690 a(3) = 70 = (1, 3, 3, 1) dot (1, 6, 14, 9) = (1 + 18 + 42 + 9). a(3) = 70 = sum of row 3 terms of triangle A033292: (13 + 16 + 19, + 22).
%t A143690 Table[(n+1)*(3*n^2+2*n+2)/2, {n,0,50}] (* _G. C. Greubel_, May 30 2021 *)
%o A143690 (Sage) [(n+1)*(3*n^2+2*n+2)/2 for n in (0..50)] # _G. C. Greubel_, May 30 2021
%Y A143690 Cf. A000292, A000326, A002412, A033292.
%Y A143690 Cf. A226449. - _Bruno Berselli_, Jun 09 2013
%K A143690 nonn,easy
%O A143690 0,2
%A A143690 _Gary W. Adamson_, Aug 29 2008
%E A143690 Extended beyond a(14) by _R. J. Mathar_, Aug 29 2008