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A294034 Triangle read by rows, expansion of exp(x*z)*z*((exp(z) + 1)/((exp(z) + 2*exp(-z/2)*cos(z*sqrt(3)/2))/3) -1), for n >= 1 and 0 <= k <= n-1. 1
1, 2, 2, 3, 6, 3, -4, 12, 12, 4, -15, -20, 30, 20, 5, -54, -90, -60, 60, 30, 6, 133, -378, -315, -140, 105, 42, 7, 792, 1064, -1512, -840, -280, 168, 56, 8, 4293, 7128, 4788, -4536, -1890, -504, 252, 72, 9, -15130, 42930, 35640, 15960, -11340, -3780, -840, 360, 90, 10, -123849, -166430, 236115, 130680, 43890, -24948, -6930, -1320, 495, 110, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Triangle starts:

[1][   1]

[2][   2,    2]

[3][   3,    6,     3]

[4][  -4,   12,    12,    4]

[5][ -15,  -20,    30,   20,    5]

[6][ -54,  -90,   -60,   60,   30,   6]

[7][ 133, -378,  -315, -140,  105,  42,  7]

[8][ 792, 1064, -1512, -840, -280, 168, 56, 8]

MAPLE

gf := exp(x*z)*z*((exp(z) + 1)/((exp(z) + 2*exp(-z/2)*cos(z*sqrt(3)/2))/3) - 1):

s := n -> n!*coeff(series(gf, z, 12), z, n):

C := n -> PolynomialTools:-CoefficientList(s(n), x):

ListTools:-FlattenOnce([seq(C(n), n=1..11)]);

CROSSREFS

Cf. A003506, A294033.

Sequence in context: A003506 A047662 A183474 * A210220 A075196 A196912

Adjacent sequences:  A294031 A294032 A294033 * A294035 A294036 A294037

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Oct 24 2017

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)