A032317 Shifts left under "EGJ" (unordered, element, labeled) transform.

1, 1, 1, 4, 8, 38, 206, 1200, 7244, 55112, 481108, 4287064, 42556692, 458857096, 5380649292, 66715285656, 886324380896, 12515424567584, 187185185162008, 2950679797693984, 48999725880417856, 854663308052386560, 15612043048565029376, 298116231774768917120

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

C. G. Bower, Transforms (2)

Formula

a(n) ~ d^n * (n-1)!, where d = 0.83032081103345967620460720103738024... . - Vaclav Kotesovec, Aug 25 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(multinomial(n, i$j, n-i*j)*binomial(b((i-1)$2), j)
       *b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b((n-1)$2):
seq(a(n), n=1..30);  # Alois P. Heinz, Jul 30 2013

Mathematica

multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[multinomial[n, Append[Array[i&, j], n-i*j]]*Binomial[ b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n-1, n-1]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 27 2017, after Alois P. Heinz *)

Prog

(PARI) EGJ(v)={Vec(serlaplace(prod(k=1, #v, (1 + x^k/k! + O(x*x^#v))^v[k]))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, v=concat([1], EGJ(v))); v} \\ Andrew Howroyd, Sep 11 2018
(PARI) seq(n)={my(p=(1+x) + O(x^n)); for(k=2, n-1, p*=(1 + x^k/k! + O(x^n))^((k-1)!*polcoef(p, k-1))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 20 2018

Crossrefs

Sequence in context: A032301 A032213 A225824 * A032226 A001889 A032138

Adjacent sequences: A032314 A032315 A032316 * A032318 A032319 A032320

Keyword

nonn,eigen

Author

Christian G. Bower

Status

approved