OFFSET
0,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..525
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/4)} (4*k+1) * a(k) * a(n-1-4*k) / (24^k * k! * (n-1-4*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-4)(x^4/24)), x, n+1), polynom), x) fi
end:
a:= n-> coeff(A(n)(x), x, n)*n!:
seq(a(n), n=0..30);
MATHEMATICA
A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^4/4!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 13 2014, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 24 2008
STATUS
approved