OFFSET
0,3
COMMENTS
Exponential transform of A000009.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..550
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: exp(Sum_{k>=1} A000009(k)*x^k/k!).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 2*x^2/2! + 6*x^3/3! + 20*x^4/4! + 79*x^5/5! + 358*x^6/6! + 1791*x^7/7! + ...
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
`if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*b(j), j=1..n))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 07 2018
MATHEMATICA
nmax = 24; CoefficientList[Series[Exp[Sum[PartitionsQ[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[PartitionsQ[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 07 2018
STATUS
approved