OFFSET
0,2
FORMULA
a(n)=sum(k=1..n, binomial(2*n,k)*(i=0..k/2, sum((2*i-k)^(2*n-k)*binomial(k,i)*(-1)^(n-i)))/(2^(k-1))). - Vladimir Kruchinin, Jun 06 2011
a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(k+1) * binomial(2*n-1,2*k-1) * k * a(n-k). - Ilya Gutkovskiy, Mar 10 2022
MATHEMATICA
nmax = 30; Take[CoefficientList[Series[Exp[x Sin[x]], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
PROG
(Maxima)
a(n):=sum(binomial(2*n, k)*(sum((2*i-k)^(2*n-k)*binomial(k, i)*(-1)^(n-i), i, 0, k/2))/(2^(k-1)), k, 1, n); /* Vladimir Kruchinin, Jun 06 2011 */
(PARI) my(x='x+O('x^40), v=Vec(serlaplace(exp(x*sin(x))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved