A171685 Triangle T(n,k) which contains 16*n!*2^floor((n+1)/2) times the coefficient [t^n x^k] exp(t*x)/(15 + exp(8*t)) in row n, column k.

1, -1, 2, -7, -2, 2, -83, -42, -6, 4, -266, -332, -84, -8, 4, 5666, -2660, -1660, -280, -20, 8, 146762, 33996, -7980, -3320, -420, -24, 8, 3415978, 2054668, 237972, -37240, -11620, -1176, -56, 16, 7599256, 27327824, 8218672, 634592, -74480

Offset

0,3

Comments

The bivariate taylor expansion of exp(t*x)/(15+exp(8*t)) is 1/16 + (x/16-1/32)*t +(-7/64+x^2/32 -x/32)*t^2+ (-83/384+x^3/96-7*x/64-x^2/64)*t^3+...

Row n contains the coefficients of the polynomial in front of t^n, multiplied by 16*floor[(n+1)/2]*n!.

Row sums are: 1, 1, -7, -127, -686, 1054, 169022, 5658542, 43685656, -1052651384, -55785840712,....

Links

Table of n, a(n) for n=0..40.

Example

The triangle starts in row n=0 with columns 0<=k <=n as
1;
-1, 2;
-7, -2, 2;
-83, -42, -6, 4;
-266, -332, -84, -8, 4;
5666, -2660, -1660, -280, -20, 8;
146762, 33996, -7980, -3320, -420, -24, 8;
3415978, 2054668, 237972, -37240, -11620, -1176, -56, 16;
7599256, 27327824, 8218672, 634592, -74480, -18592, -1568, -64, 16;
-1487228056, 136786608, 245950416, 49312032, 2855664, -268128, -55776, -4032, -144, 32;
-42545787592, -14872280560, 683933040, 819834720, 123280080, 5711328, -446880, -79680, -5040, -160, 32;

Mathematica

Clear[p, g, m, a];
m = 3;
p[t_] = 2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[2^m*t])
Table[ FullSimplify[ExpandAll[2^ Floor[(n + 1)/2]*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], {n, 0, 10}]
a = Table[CoefficientList[FullSimplify[ExpandAll[2^Floor[(n + 1)/2]*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]
Flatten[a]

Crossrefs

Cf. A000364, A171684.

Sequence in context: A073246 A021790 A266390 * A011048 A307671 A011401

Adjacent sequences: A171682 A171683 A171684 * A171686 A171687 A171688

Keyword

sign,tabl

Author

Roger L. Bagula, Dec 15 2009

Extensions

Number of variables in use reduced from 4 to 2, keyword:tabl added - The Assoc. Eds. of the OEIS, Oct 20 2010

Status

approved