A143635 E.g.f. satisfies: A(x) = exp(x*A(((x+1)^4-1)/4)).

1, 1, 3, 25, 329, 6471, 175747, 6222259, 277683681, 15206462497, 1000136567591, 77666331244239, 7021789807671817, 730394622232111747, 86529393614846902371, 11573498785704862459891, 1734360074041552070631713

Offset: 0

Author

Alois P. Heinz, Aug 27 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. 4th column of A143632.

Programs

Maple

A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,4)(x), x,n)*n!: seq(a(n), n=0..21);

Mathematica

A[n_, k_] := A[n, k] = Module[{f}, f = Function[If[n <= 0 || k == 0, 1, A[n-1, k][((#+1)^k-1)/k]]]; Function[Normal[Series[Exp[x*f[x]], {x, 0, n+1}]] /. x -> #]]; a[n_] := SeriesCoefficient[A[n, 4][x], {x, 0, n}]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 13 2014, after Maple *)