A291976 a(n) = (4*n)! * [z^(4*n)] exp(1 - (cos(z) + cosh(z))/2).

1, -1, 34, -5281, 2185429, -1854147586, 2755045819549, -6440372006517541, 21861211462545555394, -100916681831006840635021, 596756926975162013357972089, -4237398636260867429185819175026, 32919774165127854788267224335178009

Offset: 0

Author

Peter Luschny, Sep 07 2017

Keywords

• sign

Comments

Alternating row sums of A291452.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..155

Crossrefs

Cf. A291452.

Programs

Maple

A291976 := proc(n) exp(1 - (cos(z) + cosh(z))/2):
(4*n)!*coeff(series(%, z, 4*(n+1)), z, 4*n) end:
seq(A291976(n), n=0..12);
# second Maple program:
b:= proc(n, t) option remember; `if`(n=0, 1-2*t, add(
      b(n-4*j, 1-t)*binomial(n-1, 4*j-1), j=1..n/4))
    end:
a:= n-> b(4*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-4j, 1-t] * Binomial[n-1, 4j-1], {j, 1, n/4}]];
a[n_] := b[4n, 0];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 27 2023, after Alois P. Heinz *)