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A355338
Expansion of e.g.f.: exp(exp(x) - x^2 - 1).
2
1, 1, 0, -1, 3, 12, -7, -47, 332, 1347, -2105, -4200, 135457, 474697, -900832, 4682135, 126196787, 439488524, 233313817, 19129265609, 239146712732, 1104038984091, 5891696027079, 89831511761320, 911995655018817, 6253185308181553, 54873149768926624, 653039078246798383
OFFSET
0,5
LINKS
FORMULA
a(n) ~ n^n * exp(n/LambertW(n) - LambertW(n)^2 - n - 1) / (sqrt(1 + LambertW(n)) * LambertW(n)^n).
a(n) ~ Bell(n) / exp(LambertW(n)^2).
a(0) = a(1) = 1; a(n) = -2 * (n-1) * a(n-2) + Sum_{k=1..n} binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, Jun 29 2022
MATHEMATICA
nmax = 30; CoefficientList[Series[Exp[Exp[x] - x^2 - 1], {x, 0, nmax}], x] * Range[0, nmax]!
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(exp(x) - x^2 - 1))) \\ Michel Marcus, Jun 29 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Jun 29 2022
STATUS
approved