A144792 EXP transform of A140585.

1, 1, 5, 33, 282, 2938, 36029, 507440, 8058990, 142315830, 2763775025, 58498072273, 1339545500214, 32980132065364, 868417100538399, 24344702489881998, 723694354351500431, 22733368105181643193, 752291980101845144878, 26153153055424960528533

Offset

0,3

Comments

Stirling transform of A143463.

Links

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

Formula

E.g.f: (1/exp(1)) exp( 1 / prod_{k=1}^{inf} (1 - (exp(x)-1)^k / k!) ).

a(n) = sum_{k=1..n} C(n-1,k-1) A140585(k) a(n-k).

With S2(n,k) as the Stirling number of the second kind we have

a(n) = sum_{k=1..n} A143463(n) S2(n,k).

Maple

with(numtheory): with(combinat): b:= proc(k) option remember; add(d/d!^(k/d), d=divisors(k)) end: c:= proc(n) option remember; `if`(n=0, 1, add((n-1)!/(n-k)!* b(k)* c(n-k), k=1..n)) end: aa:= n-> add(stirling2(n, k) *c(k), k=1..n): a:= proc(n) option remember; `if`(n=0, 1, aa(n)+ add(binomial(n-1, k-1) *aa(k) *a(n-k), k=1..n-1)) end: seq(a(n), n=1..20); # Alois P. Heinz, Oct 10 2008

Mathematica

b[k_] := b[k] = DivisorSum[k, #/#!^(k/#)&]; c[n_] := c[n] = If[n==0, 1, Sum[(n-1)!/(n-k)!*b[k]*c[n-k], {k, 1, n}]]; aa[n_] := Sum[StirlingS2[n, k]*c[k], {k, 1, n}]; a[n_] := a[n] = If[n==0, 1, aa[n] + Sum[Binomial[ n-1, k-1]*aa[k]*a[n-k], {k, 1, n-1}]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 25 2017, after Alois P. Heinz *)

Crossrefs

Cf. A140585, A143463.

Sequence in context: A378091 A120733 A218496 * A291846 A255927 A001828

Adjacent sequences: A144789 A144790 A144791 * A144793 A144794 A144795

Keyword

nonn

Author

Thomas Wieder, Sep 21 2008

Extensions

More terms from Alois P. Heinz, Oct 10 2008

Status

approved