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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 Seiichi Manyama, Table of n, a(n) for n = 0..560 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 Cf. A003727, A352252. Sequence in context: A256905 A294547 A294557 * A012213 A012251 A084547 Adjacent sequences: A009186 A009187 A009188 * A009190 A009191 A009192 KEYWORD sign,easy AUTHOR R. H. Hardin 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.)