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A143567
E.g.f. satisfies A(x) = exp(x*A(x^3/3!)).
5
1, 1, 1, 1, 5, 21, 61, 211, 1401, 8065, 37241, 240021, 1997821, 14657501, 105629525, 958412911, 9201199281, 86311594881, 871038486001, 9432024424585, 106531641929781, 1271523772132741, 15583607760968941, 194983864950339851
OFFSET
0,5
LINKS
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/3)} (3*k+1) * a(k) * a(n-1-3*k) / (6^k * k! * (n-1-3*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-3)(x^3/6)), x, n+1), polynom), x) fi end: a:= n-> coeff (A(n)(x), x, n)*n!: seq(a(n), n=0..29);
MATHEMATICA
A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^3/3!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient [A[n][x], x, n]*n!; Table[a[n], {n, 0, 29}] (* Jean-François Alcover, Feb 13 2014, after Maple *)
CROSSREFS
3rd column of A143565.
Cf. A367719.
Sequence in context: A303170 A287617 A354551 * A147375 A351934 A356328
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 24 2008, Aug 25 2008
STATUS
approved