|
%I #21 Sep 21 2018 02:20:39
%S 1,1,1,4,8,38,206,1200,7244,55112,481108,4287064,42556692,458857096,
%T 5380649292,66715285656,886324380896,12515424567584,187185185162008,
%U 2950679797693984,48999725880417856,854663308052386560,15612043048565029376,298116231774768917120
%N Shifts left under "EGJ" (unordered, element, labeled) transform.
%H Alois P. Heinz, <a href="/A032317/b032317.txt">Table of n, a(n) for n = 1..200</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%F a(n) ~ d^n * (n-1)!, where d = 0.83032081103345967620460720103738024... . - _Vaclav Kotesovec_, Aug 25 2014
%p with(combinat):
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(multinomial(n, i$j, n-i*j)*binomial(b((i-1)$2), j)
%p *b(n-i*j, i-1), j=0..n/i)))
%p end:
%p a:= n-> b((n-1)$2):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Jul 30 2013
%t 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_ *)
%o (PARI) EGJ(v)={Vec(serlaplace(prod(k=1, #v, (1 + x^k/k! + O(x*x^#v))^v[k]))-1, -#v)}
%o seq(n)={my(v=[1]); for(n=2, n, v=concat([1], EGJ(v))); v} \\ _Andrew Howroyd_, Sep 11 2018
%o (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
%K nonn,eigen
%O 1,4
%A _Christian G. Bower_
|
