A179087 - OEIS

%I #15 May 04 2019 23:07:00

%S 1,1,1,-3,14,-3,-11,35,35,-11,-7,-84,566,-84,-7,41,-843,2722,2722,

%T -843,41,117,-2854,763,50028,763,-2854,117,29,-4681,-80211,407423,

%U 407423,-80211,-4681,29,-527,4504,-720740,1560616,8634214,1560616,-720740,4504,-527,-1199,68393,-4275340,-6925948,104031374,104031374,-6925948,-4275340,68393,-1199,237,338918,-19903639,-195090616,799237802,2546725796,799237802,-195090616

%N Triangle T(n,k) read by rows: the real part of the coefficient [x^k] of (1-x)^(n+1) * Sum_{s>=0} ((2*s + 1 + 2*i)^n)*x^s, where i is the imaginary unit.

%e Triangle begins

%e     1;

%e     1,     1;

%e    -3,    14,     -3;

%e   -11,    35,     35,    -11;

%e    -7,   -84,    566,    -84,     -7;

%e    41,  -843,   2722,   2722,   -843,     41;

%e   117, -2854,    763,  50028,    763,  -2854,   117;

%e    29, -4681, -80211, 407423, 407423, -80211, -4681, 29;

%p A179087 := proc(n,k)

%p         (1-x)^(n+1)*add( (2*s+1+2*I)^n*x^s,s=0..k) ;

%p         expand(%) ;

%p         coeftayl(%,x=0,k) ;

%p         Re(%) ;

%p end proc: # _R. J. Mathar_, Oct 06 2011

%Y Cf. A000165 (row sums), A006495 (column k=0).

%K sign,tabl

%O 0,4

%A _Roger L. Bagula_, Jun 28 2010

%E Sequence replaced with one that is more likely to occur in practice by _R. J. Mathar_, Oct 06 2011