A185074 Number of representations of n in the form sum(i=1..n, c(i)/i ), where each of the c(i)'s is in {0,1,...,n}.

1, 2, 4, 16, 36, 447, 1274, 9443, 54094, 995169, 3013040, 79403971, 244277081, 5853252222, 171545158710, 2586069434760, 8747524457442, 290539678831816, 1002826545775653, 37782799964911391, 1405277934671848125, 53429557586727235246, 189496067102901557686

Offset: 1

Author

John W. Layman, Mar 02 2012

Keywords

• nonn

Examples

			For n=3, 1/1+2/2+3/3 = 2/1+0/2+3/3 = 2/1+2/2+0/3 = 3/1+0/2+0/3 = 3 and no other sums of the required type give 3, so a(3)=4.  For n=4, 0/1+4/2+3/3+4/4 and 15 other sums of the required type give 4, so a(4)=16.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..26

Crossrefs

Cf. A002966, A020473.

Programs

Maple

b:= proc(r, i, n) option remember;
      `if`(r=0, 1, `if`(i>n, 0,
      add(b(r-j/i, i+1, n), j=0..min(n, r*i))))
    end:
a:= n-> b(n, 1, n):
seq(a(n), n=1..10);  # Alois P. Heinz, Mar 06 2012

Mathematica

b[r_, i_, n_] := b[r, i, n] = If[r == 0, 1, If[i>n, 0, Sum[b[r-j/i, i+1, n], {j, 0, Min[n, r*i]}]]]; a[n_] := b[n, 1, n]; Table[Print[a[n]]; a[n], {n, 1, 13}] (* Jean-François Alcover, Feb 27 2014, after Alois P. Heinz *)

PARI

A185074(n,i=1,m)={n || return(1); m || m=n; i>m & return; sum(j=0,min(m, n*i),A185074(n-j/i, i+1, m))} \\ - M. F. Hasler, Mar 07 2012

PARI

/* version with memoization - seems not faster */ R185074=Set("[0]"); A185074(n,i=1,m)={n || return(1); m || m=n; i>m & return; my(t=eval(R185074[setsearch(R185074,[n,i,m],1)-1])); t[1]==n & t[2]==i & t[3]==m & return(t[4]); t=sum(j=0,min(m, n*i),A185074(n-j/i, i+1, m)); R185074=setunion(R185074,Set([[n,i,m,t]])); t} \\ - M. F. Hasler, Mar 07 2012

Extensions

a(7)-a(10) from R. J. Mathar, a(11)-a(13) from Alois P. Heinz, Mar 06 2012

a(14) from Alois P. Heinz, Sep 27 2014

a(15)-a(23) from Hiroaki Yamanouchi, Oct 03 2014