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A352642
Expansion of e.g.f. exp(2 * x * cos(x)).
4
1, 2, 4, 2, -32, -198, -416, 2634, 30720, 107378, -605696, -10282094, -46020608, 304968874, 6121832448, 29994597338, -279697555456, -5729595393310, -26849178681344, 401845799334690, 7714801999937536, 29062583111892506, -812705956979802112
OFFSET
0,2
LINKS
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
MATHEMATICA
With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[2*x*Cos[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*x*cos(x))))
(PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
CROSSREFS
Sequence in context: A295640 A210457 A006496 * A361077 A263931 A375902
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 25 2022
STATUS
approved