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A032317 Shifts left under "EGJ" (unordered, element, labeled) transform. 1
1, 1, 1, 4, 8, 38, 206, 1200, 7244, 55112, 481108, 4287064, 42556692, 458857096, 5380649292, 66715285656, 886324380896, 12515424567584, 187185185162008, 2950679797693984, 48999725880417856, 854663308052386560, 15612043048565029376, 298116231774768917120 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)