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A317677 Fixed point of a shifted hypertree transform. 5
1, 1, 4, 32, 402, 7038, 160114, 4522578, 153640590, 6132546770, 282517271694, 14812447505646, 873934551644074, 57486823088667270, 4183353479821220130, 334572221351085006242, 29242220614539638127294, 2779426070382982579163202, 286058737295150226682469518 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The hypertree transform H(a) of a sequence a is given by H(a)(n) = Sum_p n^(k-1) Prod_i a(|p_i|+1), where the sum is over all set partitions U(p_1, ..., p_k) = {1, ..., n-1}.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..305

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1/k, add(

      a(j)*b(n-j, k)*binomial(n-1, j-1)*k, j=1..n))

    end:

a:= n-> b(n-1, n):

seq(a(n), n=1..20);  # Alois P. Heinz, Aug 21 2019

MATHEMATICA

numSetPtnsOfType[ptn_]:=Total[ptn]!/Times@@Factorial/@ptn/Times@@Factorial/@Length/@Split[ptn];

a[n_]:=a[n]=Sum[n^(Length[ptn]-1)*numSetPtnsOfType[ptn]*Product[a[s], {s, ptn}], {ptn, IntegerPartitions[n-1]}];

Array[a, 20]

(* Second program: *)

b[n_, k_] := b[n, k] = If[n == 0, 1/k, Sum[

     a[j]*b[n - j, k]*Binomial[n - 1, j - 1]*k, {j, 1, n}]];

a[n_] := b[n - 1, n];

Array[a, 20] (* Jean-Fran├žois Alcover, May 10 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A000272, A030019, A048143, A134954, A275307, A293510, A317631, A317632, A317634, A317635, A317671.

Sequence in context: A127670 A317403 A243468 * A191459 A184359 A229548

Adjacent sequences:  A317674 A317675 A317676 * A317678 A317679 A317680

KEYWORD

nonn,eigen

AUTHOR

Gus Wiseman, Aug 04 2018

STATUS

approved

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Last modified June 16 19:02 EDT 2021. Contains 345068 sequences. (Running on oeis4.)