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A143566
E.g.f. satisfies A(x) = exp(x*A(x^2/2!)).
3
1, 1, 1, 4, 13, 46, 241, 1471, 9409, 67348, 564841, 4771801, 45459481, 463867834, 5060656693, 58878140686, 730612429681, 9556314730456, 131627520296929, 1912237000523623, 29032781640572881, 462811831018070206, 7687624300327129621, 133275225843052767244
OFFSET
0,4
LINKS
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/2)} (2*k+1) * a(k) * a(n-1-2*k) / (2^k * k! * (n-1-2*k)!). - Seiichi Manyama, Nov 28 2023
MAPLE
A:= proc(n) option remember; if n<=0 then 1 else unapply(convert(
series(exp(x*A(n-2)(x^2/2)), x, n+1), polynom), x) fi
end:
a:= n-> coeff(A(n)(x), x, n)*n!:
seq(a(n), n=0..28);
MATHEMATICA
A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^2/2]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Feb 13 2014, after Maple *)
CROSSREFS
2nd column of A143565.
Cf. A138292.
Sequence in context: A149439 A014145 A354550 * A098841 A363547 A017944
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 24 2008
STATUS
approved