%I A105277
%S A105277 0,1,5,29,203,1680,16058,173865,2099957,27952999,406125305,6389713034,
%T A105277 108157272720,1958821525361,37779732341077,772829270394685,
%U A105277 16708083353842267,380563529091632760,9106983116342966818
%N A105277 Let b(n) denote the Fibonacci numbers, A000045: a(n) = Sum{k=0..n}C(n,
               k)^2*(n-k)!*b(k).
%C A105277 If E.g.f. of b(n) is E(x) and a(n) = Sum{k=0..n}C(n,k)^2*(n-k)!*b(k), 
               then E.g.f. of a(n) is E(x/(1-x))/(1-x).
%F A105277 E.g.f.: (2/sqrt(5))*exp(x/2/(1-x))*sinh(sqrt(5)*x/2/(1-x))/(1-x).
%e A105277 b(n) = 0,1,1,2,3,5,8,13,21,34,55,...
%e A105277 a(3) = C(3,0)^2*3!*b(0)+C(3,1)^2*2!*b(1)+C(3,2)^2*1!*b(2)+C(3,3)^2*0!*b(3) 
               = 1*6*0+9*2*1+9*1*1+1*1*2 = 0+18+9+2 = 29
%p A105277 b[0]:=0:b[1]:=1:for n from 2 to 30 do b[n]:=b[n-1]+b[n-2] od: seq(sum('binomial(n,
               k)^2*(n-k)!*b[k]', 'k'=0..n),n=0..30);
%Y A105277 Cf. A000045.
%Y A105277 Sequence in context: A094710 A108453 A004213 this_sequence A103213 A057588 
               A030522
%Y A105277 Adjacent sequences: A105274 A105275 A105276 this_sequence A105278 A105279 
               A105280
%K A105277 easy,nonn
%O A105277 0,3
%A A105277 Miklos Kristof (kristmikl(AT)freemail.hu), Apr 25 2005