A143572 E.g.f. satisfies A(x) = exp(x*A(x^8/8!)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 91, 496, 1981, 6436, 18019, 45046, 102961, 328186, 4375801, 56951038, 500352841, 3276290746, 17289324361, 77309034166, 302908144177, 1104328093276, 7519851360451, 134741602227376, 2095457847783301, 23492070829121896

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/8)} (8*k+1) * a(k) * a(n-1-8*k) / (40320^k * k! * (n-1-8*k)!). - Seiichi Manyama, Nov 29 2023

Maple

A:= proc(n) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-8)(x^8/40320)), x, n+1), polynom), x) fi end: a:= n-> coeff (A(n)(x), x, n)*n!: seq(a(n), n=0..35);

Mathematica

A[n_] := A[n] = If[n <= 0, 1&, Function[Normal[Series[Exp[y*A[n-2][y^8/8!]], {y, 0, n+1}] /. y -> #]]]; a[n_] := Coefficient[A[n][x], x, n]*n!; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 13 2014, after Maple *)

Crossrefs

8th column of A143565.

Sequence in context: A175710 A226389 A119047 * A365305 A244203 A002739

Adjacent sequences: A143569 A143570 A143571 * A143573 A143574 A143575

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2008

Status

approved