A086951 - OEIS

%I #11 Apr 10 2023 10:25:40

%S 0,1,14,99,540,2565,11178,45927,180792,688905,2558790,9310059,

%T 33303636,117448461,409209570,1410975855,4821232752,16343405073,

%U 55013709438,184024732275,612124372620,2025821736981,6673705343514,21893519253879,71548815908520,233004367596825

%N a(n) = n*3^n*(4*n - 1)/9.

%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 + 5*x)/(1 - 3*x)^3.

%F E.g.f.: exp(3*x)*x*(1 + 4*x). - _Stefano Spezia_, Oct 09 2022

%t LinearRecurrence[{9,-27,27},{0,1,14},30] (* _Harvey P. Dale_, Apr 10 2023 *)

%Y Binomial transform of A086950. Second binomial transform of decagonal numbers A001107. Binomial transform is A086952.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Jul 24 2003