%I #11 Jan 09 2015 20:59:24

%S 1,10,49,142,313,586,985,1534,2257,3178,4321,5710,7369,9322,11593,

%T 14206,17185,20554,24337,28558,33241,38410,44089,50302,57073,64426,

%U 72385,80974,90217,100138,110761,122110,134209,147082,160753,175246

%N a(n) = 1 + 2n + 3n^2 + 4n^3.

%F a(n) = (A053699(n+1) - A053699(n-1))/2 - 4n - 1.

%F G.f.: (1 + 6*x + 15*x^2 + 2*x^3)/(1-x)^4. - _Colin Barker_, Jan 10 2012

%e For n>4 this is 4321 translated from base n to base 10.

%t f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst,f[n]],{n,0,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2010 *)

%Y Note: 1 + 2x + 3x^2 + 4x^3 is the first derivative of 1 + x + x^2 + x^3 + x^4, i.e., A053699. Cf. A000012, A005408, A056109, A056579.

%K easy,nonn

%O 0,2

%A _Henry Bottomley_, Jun 29 2000