%I A099364
%S A099364 1,2,2,4,5,10,14,28,42,84,132,264,429,858,1430,2860,4862,9724,16796,33592,
%T A099364 58786,117572,208012,416024,742900,1485800,2674440,5348880,9694845,19389690,
%U A099364 35357670,70715340,129644790,259289580,477638700,955277400,1767263190,
               3534526380
%V A099364 1,-2,2,-4,5,-10,14,-28,42,-84,132,-264,429,-858,1430,-2860,4862,-9724,
               16796,-33592,
%W A099364 58786,-117572,208012,-416024,742900,-1485800,2674440,-5348880,9694845,
               -19389690,
%X A099364 35357670,-70715340,129644790,-259289580,477638700,-955277400,1767263190,
               -3534526380
%N A099364 An inverse Chebyshev transform of (1-x)^2.
%C A099364 Second binomial transform of the expansion of c(-x)^4 (i.e. of (-1)^n*4C(2n+3,
               n)/(n+4)). The g.f. is transformed to (1-x)^2 under the Chebyshev 
               transformation A(x)->(1/(1+x^2))A(x/(1+x^2)).
%F A099364 G.f.: (c(x^2)-1)(1-2x)/x^2 with c(x) the g.f. of A000108; a(n)=sum{k=0..n, 
               (k+1)C(n, (n-k)/2)(-1)^k*C(2, k)(1+(-1)^(n-k))/(n+k+2)}; a(n)=sum{k=0..n, 
               (k+1)C(n, (n-k)/2)b(k)(1+(-1)^(n-k))/(n+k+2)} where b(n)=0^n+sum{k=0..n, 
               C(n, k)(-1)^(n-k)(-3k+k(k+1)/2)}; a(2n)=C(n+1); a(2n+1)=-2*C(n+1).
%Y A099364 Cf. A089408, A002057.
%Y A099364 Sequence in context: A032090 A000014 A114851 this_sequence A125951 A054538 
               A095020
%Y A099364 Adjacent sequences: A099361 A099362 A099363 this_sequence A099365 A099366 
               A099367
%K A099364 easy,sign
%O A099364 0,2
%A A099364 Paul Barry (pbarry(AT)wit.ie), Oct 13 2004