A139488 - OEIS

%I #16 Aug 17 2022 11:21:08

%S 1,3,8,20,43,81,138,218,325,463,636,848,1103,1405,1758,2166,2633,3163,

%T 3760,4428,5171,5993,6898,7890,8973,10151,11428,12808,14295,15893,

%U 17606,19438,21393,23475,25688,28036,30523,33153,35930,38858,41941,45183

%N Binomial transform of [1, 2, 3, 4, 0, 0, 0, ...].

%F Equals A007318 * [1, 2, 3, 4, 0, 0, 0, ...].

%F a(n) = (4n^3 - 3n^2 + 11n + 6)/6. - _Emeric Deutsch_, Apr 30 2008

%F G.f.: (1 - x + 2*x^2 + 2*x^3)/(1-x)^4. - _Colin Barker_, Feb 01 2012

%e a(5) = 43 = (1, 4, 6, 4, 1) dot (1, 2, 3, 4, 0) = (1 + 8, + 18 + 16 + 0).

%p a:=proc(n) options operator, arrow: (2/3)*n^3-(1/2)*n^2+(11/6)*n+1 end proc: seq(a(n),n=0..35); # _Emeric Deutsch_, Apr 30 2008

%t f[n_] := Plus @@ (Table[ Binomial[n - 1, i], {i, 0, n - 1}] PadRight[{1, 2, 3, 4}, n]); Array[f, 43] (* _Robert G. Wilson v_, Apr 24 2008 *)

%Y Cf. A005408, A007318, A104249, A116445.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Apr 23 2008

%E More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Apr 24 2008