A176990 Table T(n,m) read by rows: the coefficient of [t^n x^m] of 2*n!*(n+2)!*exp(x*t)*( t*(1-exp(t))-exp(t) ) / (1-exp(t) ), 0<=m<=n+1.

2, 4, 13, 6, 6, 0, 104, 24, 16, -2, 0, 780, 120, 60, 0, -48, 0, 6240, 720, 288, 40, 0, -840, 0, 54600, 5040, 1680, 0, 1920, 0, -13440, 0, 524160, 40320, 11520, -3024, 0, 60480, 0, -211680, 0, 5503680, 362880, 90720, 0, -241920, 0, 1612800, 0, -3386880, 0, 62899200, 3628800, 806400, 604800, 0, -11975040, 0, 39916800, 0, -55883520, 0, 778377600, 39916800, 7983360, 0, 72576000, 0, -479001600, 0, 958003200, 0, -958003200, 0, 10378368000, 479001600, 87091200

Offset

0,1

Comments

Row sums are: 6, 25, 144, 958, 7200, 60520, 564480, 5803056, 65318400, 798940800,

10538035200,....

The bivariate expansion is exp(x*t)*( t*(1-exp(t))-exp(t) )/ (1-exp(t) )= 1/t +(1/2+x)*t^0 + (13/12+x/2+x^2/2)*t +... The leading term 1/t corresponding to n = -1 is dropped, and the other rows are scaled with a factor 2*n!*(n+2)!.

Links

Table of n, a(n) for n=0..76.

Example

2, 4;
13, 6, 6;
0, 104, 24, 16;
-2, 0, 780, 120, 60;
0, -48, 0, 6240, 720, 288;
40, 0, -840, 0, 54600, 5040, 1680;
0,1920, 0, -13440, 0, 524160, 40320, 11520;
-3024, 0, 60480, 0, -211680, 0, 5503680, 362880, 90720;
0, -241920, 0, 1612800, 0, -3386880, 0, 62899200, 3628800, 806400;
604800, 0, -11975040, 0, 39916800, 0, -55883520, 0, 778377600, 39916800, 7983360;
0,72576000, 0, -479001600, 0, 958003200, 0, -958003200, 0, 10378368000, 479001600, 87091200;

Mathematica

p[t_] = Exp[x*t](t*(1 - Exp[t]) - Exp[t])/(1 - Exp[t]);
a = Table[ CoefficientList[(n!*(n + 2)!*2)*SeriesCoefficient[
      Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
Flatten[a]

Crossrefs

Cf. A176989.

Sequence in context: A030064 A224886 A180500 * A109928 A023640 A367109

Adjacent sequences: A176987 A176988 A176989 * A176991 A176992 A176993

Keyword

sign,tabf

Author

Roger L. Bagula, Dec 08 2010

Status

approved