cp's OEIS Frontend

A145118 Denominator polynomials for continued fraction generating function for n!.

%I A145118 #6 Dec 04 2012 20:21:14
%S A145118 1,1,1,-1,1,-2,1,-4,2,1,-6,6,1,-9,18,-6,1,-12,36,-24,1,-16,72,-96,24,
%T A145118 1,-20,120,-240,120,1,-25,200,-600,600,-120,1,-30,300,-1200,1800,-720,
%U A145118 1,-36,450,-2400,5400,-4320,720,1,-42,630,-4200,12600,-15120
%N A145118 Denominator polynomials for continued fraction generating function for n!.
%C A145118 Row sums are A056920. T(n,1) gives quarter squares A002620. T(n,2) appears to coincide with 2*A000241(n+1).
%H A145118 Alois P. Heinz, <a href="/A145118/b145118.txt">Rows n = 0..200, flattened</a>
%F A145118 T(n,k) = (-1)^k C(floor((n+1)/2),k) * C(floor(n/2),k)*k!.
%e A145118 Triangle begins:
%e A145118 1;
%e A145118 1;
%e A145118 1,  -1;
%e A145118 1,  -2;
%e A145118 1,  -4,   2;
%e A145118 1,  -6,   6;
%e A145118 1,  -9,  18,    -6;
%e A145118 1, -12,  36,   -24;
%e A145118 1, -16,  72,   -96,   24;
%e A145118 1, -20, 120,  -240,  120;
%e A145118 1, -25, 200,  -600,  600,  -120;
%e A145118 1, -30, 300, -1200, 1800,  -720;
%e A145118 1, -36, 450, -2400, 5400, -4320, 720;
%p A145118 T:= (n, k)-> (-1)^k* binomial(iquo(n+1, 2),k) *binomial(iquo(n, 2), k)*k!:
%p A145118 seq (seq (T(n, k), k=0..iquo(n, 2)), n=0..16);  # _Alois P. Heinz_, Dec 04 2012
%Y A145118 Cf. A021010, A008297, A066667, A105278.
%K A145118 easy,sign,tabf
%O A145118 0,6
%A A145118 _Paul Barry_, Oct 02 2008