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A009189 Expansion of e.g.f.: exp(cos(x)*x). 8
1, 1, 1, -2, -11, -24, 61, 624, 1737, -7424, -88679, -242560, 2086525, 23499776, 45950997, -1002251264, -9763133167, -2151563264, 705668046769, 5583112077312, -17356978593659, -666018502836224, -3823112141007763, 39230927775531008, 788728947108214489 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = (sum(k=1..n-1, binomial(n,k)*(-1)^((n-k)/2)*(1+(-1)^(n-k))/(2^(k))*sum(i=0..floor((k-1)/2)), binomial(k,i)*(k-2*i)^(n-k)))+1. - Vladimir Kruchinin, Apr 21 2011
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * (2*k+1) * a(n-2*k-1). - Ilya Gutkovskiy, Mar 10 2022
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[Cos[x]*x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 15 2018 *)
PROG
(Maxima) a(n):=(sum(binomial(n, k)*(-1)^((n-k)/2)*(1+(-1)^(n-k))/(2^(k))*sum(binomial(k, i)*(k-2*i)^(n-k), i, 0, floor((k-1)/2)), k, 1, n-1))+1; /* Vladimir Kruchinin, Apr 21 2011 */
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*cos(x)))) \\ Seiichi Manyama, Mar 26 2022
CROSSREFS
Sequence in context: A256905 A294547 A294557 * A012213 A012251 A084547
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Mar 15 2018
STATUS
approved

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Last modified February 25 02:17 EST 2024. Contains 370308 sequences. (Running on oeis4.)