Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Oct 28 2023 11:32:38
%S 0,1,11,72,378,1755,7533,30618,119556,452709,1673055,6062364,21611934,
%T 75996063,264126177,908764110,3099363912,10489051017,35255264499,
%U 117775828656,391294693890,1293597012771,4257363753621,13954111172802
%N a(n) = 3^(n-2)*n*(5*n+1)/2.
%C Binomial transform of A084899. Second binomial transform of heptagonal numbers A000566. Third binomial transform of (0,1,5,0,0,0,...).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-27,27).
%F G.f.: x*(1 + 2*x)/(1 - 3*x)^3.
%F E.g.f.: exp(3*x)*x*(2 + 5*x)/2. - _Stefano Spezia_, Oct 28 2023
%t Table[(3^(n-2) n(5n+1))/2,{n,0,30}] (* or *) LinearRecurrence[{9,-27,27},{0,1,11},30] (* _Harvey P. Dale_, Jul 21 2016 *)
%Y Cf. A000566, A084899, A084901.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jun 10 2003