A179087 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.

1, 1, 1, -3, 14, -3, -11, 35, 35, -11, -7, -84, 566, -84, -7, 41, -843, 2722, 2722, -843, 41, 117, -2854, 763, 50028, 763, -2854, 117, 29, -4681, -80211, 407423, 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

Offset: 0

Author

Roger L. Bagula, Jun 28 2010

Keywords

• sign
• tabl

Examples

			Triangle begins
    1;
    1,     1;
   -3,    14,     -3;
  -11,    35,     35,    -11;
   -7,   -84,    566,    -84,     -7;
   41,  -843,   2722,   2722,   -843,     41;
  117, -2854,    763,  50028,    763,  -2854,   117;
   29, -4681, -80211, 407423, 407423, -80211, -4681, 29;
		

Crossrefs

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

Programs

Maple

A179087 := proc(n,k)
        (1-x)^(n+1)*add( (2*s+1+2*I)^n*x^s,s=0..k) ;
        expand(%) ;
        coeftayl(%,x=0,k) ;
        Re(%) ;
end proc: # R. J. Mathar, Oct 06 2011

Extensions

Sequence replaced with one that is more likely to occur in practice by R. J. Mathar, Oct 06 2011