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

0,4

Links

Table of n, a(n) for n=0..62.

Example

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;

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

Crossrefs

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

Sequence in context: A016549 A147584 A163357 * A217013 A058991 A341860

Adjacent sequences: A179084 A179085 A179086 * A179088 A179089 A179090

Keyword

sign,tabl

Author

Roger L. Bagula, Jun 28 2010

Extensions

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

Status

approved