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A291974 a(n) = (3*n)! * [z^(3*n)] exp(-(exp(z)/3 + 2*exp(-z/2)*cos(z*sqrt(3)/2)/3 - 1)). 4
1, -1, 9, -197, 6841, -254801, -3000807, 3691567683, -717149457463, -3166484321001, 70729161470807849, -27375562310313650357, -6307300288015827588199, 14726712291264935798753279, -4956785715421801286491780487, -9984523503726123391084330853037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Alternating row sums of A291451.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..205

MAPLE

A291974 := proc(n) exp(-(exp(z)/3+2*exp(-z/2)*cos(z*sqrt(3)/2)/3-1)):

(3*n)!*coeff(series(%, z, 3*(n+1)), z, 3*n) end:

seq(A291974(n), n=0..15);

# second Maple program:

b:= proc(n, t) option remember; `if`(n=0, 1-2*t, add(

      b(n-3*j, 1-t)*binomial(n-1, 3*j-1), j=1..n/3))

    end:

a:= n-> b(3*n, 0):

seq(a(n), n=0..20);  # Alois P. Heinz, Aug 14 2019

CROSSREFS

Cf. A291451.

Sequence in context: A244506 A274269 A250401 * A180778 A110807 A019566

Adjacent sequences:  A291971 A291972 A291973 * A291975 A291976 A291977

KEYWORD

sign

AUTHOR

Peter Luschny, Sep 07 2017

STATUS

approved

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Last modified August 17 10:27 EDT 2022. Contains 356187 sequences. (Running on oeis4.)