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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
OFFSET
0,3
COMMENTS
Alternating row sums of A291451.
LINKS
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
MATHEMATICA
b[n_, t_] := b[n, t] = If[n == 0, 1-2t, Sum[b[n-3j, 1-t] * Binomial[n-1, 3j-1], {j, 1, n/3}]];
a[n_] := b[3n, 0];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 27 2023, after Alois P. Heinz *)
CROSSREFS
Cf. A291451.
Sequence in context: A244506 A274269 A250401 * A180778 A110807 A019566
KEYWORD
sign
AUTHOR
Peter Luschny, Sep 07 2017
STATUS
approved