OFFSET
1,4
COMMENTS
A107107 gives the row sums. - R. J. Mathar, Aug 13 2007
This array is the first one (K=1) of a family of partition number arrays called M31(1). For M31(2) see A134133 = M_3(2)/M_3.
LINKS
Jean-François Alcover after Wolfdieter Lang, Table of n, a(n) for n = 1..138
Wolfdieter Lang, First 10 rows of the array and more.
EXAMPLE
a(36) = 280/70 = 4.
As array: [1];[1,1];[2,1,1];[6,2,1,1,1];[24,6,2,2,1,1,1];[120,24,6,4,6,2,1,2,1,1,1];...
MAPLE
sortAbrSteg := proc(L1, L2) local i ; if nops(L1) < nops(L2) then RETURN(true) ; elif nops(L2) < nops(L1) then RETURN(false) ; else for i from 1 to nops(L1) do if op(i, L1) < op(i, L2) then RETURN(false) ; fi ; od ; RETURN(true) ; fi ; end: M2overM3 := proc(L) local n, k, an, resul; n := add(i, i=L) ; resul := 1 ; for k from 1 to n do an := add(1-min(abs(j-k), 1), j=L) ; resul := resul* (factorial(k-1))^an ; od ; end: A107106 := proc(n, k) local prts, m ; prts := combinat[partition](n) ; prts := sort(prts, sortAbrSteg) ; if k <= nops(prts) then M2overM3(op(k, prts)) ; else 0 ; fi ; end: for n from 1 to 10 do for k from 1 to combinat[numbpart](n) do a:=A107106(n, k) ; printf("%d, ", a) ; od; od ; # R. J. Mathar, Aug 13 2007
MATHEMATICA
aspartitions[n_] := Reverse /@ Sort[Sort /@ IntegerPartitions[n]];
A036039[n_] := n!/(Times @@ #)& /@ ((#! Range[n]^#)& /@ Function[par, Count[par, #]& /@ Range[n]] /@ aspartitions[n]);
runs[li : {__Integer}] := ((Length /@ Split[#]))&[Sort@li];
A036040[n_] := Module[{temp}, temp = Map[Reverse, Sort@(Sort /@ IntegerPartitions[n]), {1}]; Apply[Multinomial, temp, {1}]/Apply[Times, (runs /@ temp)!, {1}]];
Table[T[n], {n, 1, 10}] // Flatten
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Alford Arnold, May 12 2005
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 13 2007
a(75) and a(76) swapped (first 36, then 24) by Wolfdieter Lang, Sep 22 2008
STATUS
approved