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A326325 a(n) = 2^n*n!*([z^n] exp(x*z)*tanh(z)))(1/2). 0
0, 2, 4, -10, -56, 362, 2764, -24610, -250736, 2873042, 36581524, -512343610, -7828053416, 129570724922, 2309644635484, -44110959165010, -898621108880096, 19450718635716002, 445777636063460644, -10784052561125704810, -274613643571568682776, 7342627959965776406282 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 1 - 4^n*Euler(n, 1/4).
Let p(n, x) = -x^n + Sum_{k=0..n} binomial(n,k)*Euler(k)*(x+1)^(n-k) (the polynomials defined in A162660), then a(n) = 2^n*p(n, 1/2).
MAPLE
seq(1 - 4^n*euler(n, 1/4), n=0..21);
MATHEMATICA
p := CoefficientList[Series[Exp[x z] Tanh[z], {z, 0, 21}], z];
norm := Table[2^n n!, {n, 0, 21}]; norm (p /. x -> 1/2)
CROSSREFS
Sequence in context: A322294 A053500 A214724 * A080090 A125263 A326949
KEYWORD
sign
AUTHOR
Peter Luschny, Jun 28 2019
STATUS
approved

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Last modified February 26 07:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)