A179068 Triangle T(n,k) with the real part of [x^k] of the series (1-x)^(n+1)* sum_{j=0..infinity} (2*j+1+i)^n*x^j in row n, column k.

1, 1, 1, 0, 8, 0, -2, 26, 26, -2, -4, 48, 296, 48, -4, -4, 12, 1912, 1912, 12, -4, 0, -352, 9088, 28608, 9088, -352, 0, 8, -2056, 33000, 291608, 291608, 33000, -2056, 8, 16, -8576, 72640, 2366848, 5460064, 2366848, 72640, -8576, 16, 16, -30832, -168640

Offset

0,5

Comments

Real row sums are real-valued and in A000165.

Links

Table of n, a(n) for n=0..47.

Example

Real parts of the coefficients:
1;
1, 1;
0, 8, 0;
-2, 26, 26, -2;
-4, 48, 296, 48, -4;
-4, 12, 1912, 1912, 12, -4;
0, -352, 9088, 28608, 9088, -352, 0;
8, -2056, 33000, 291608, 291608, 33000, -2056, 8;
16, -8576, 72640, 2366848, 5460064, 2366848, 72640, -8576, 16;
16, -30832, -168640, 16173632, 76923104, 76923104, 16173632, -168640, -30832, 16;
Imaginary parts of the coefficients:
0;
1, -1;
2, 0, -2;
2, 18, -18, -2;
0, 96, 0, -96, 0;
-4, 340, 920, -920, -340, 4;
-8, 992, 9560, 0, -9560, -992, 8;
8, 2520, 68152, 105560, -105560, -68152, -2520, 8;
0, 5376, 408576, 1747200, 0, -1747200, -408576, -5376, 0;
16, 7536, 2204736, 19836096, 22312416, -22312416, -19836096, -2204736, -7536, -16;

Maple

A179068 := proc(n, k)
    (1-x)^(n+1)*add( (2*j+1+I)^n*x^j, j=0..n) ;
    coeftayl(%, x=0, k) ;
    Re(%) ;
end proc:
seq(seq(A179068(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Nov 05 2012

Mathematica

p[x_, n_] = (1 - x)^(n + 1)*Sum[((2*k + 1 + I)^n)*x^k, {k, 0, Infinity}];
Flatten[Table[Re[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}]]

Crossrefs

Cf. A060187, A000165

Sequence in context: A295330 A094240 A200093 * A144455 A251866 A300713

Adjacent sequences: A179065 A179066 A179067 * A179069 A179070 A179071

Keyword

sign,tabl,easy

Author

Roger L. Bagula, Jun 27 2010

Status

approved