3,5

P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.

G.f.: (t(1)^3-3*t(1)*t(2)+2*t(3))/6 where t(i) = Sum((x^n/(1+x^(n)))^i,n=1..inf), i=1..3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2007

mufact := proc(k, sumax) local res, c, i, j, isord, s ; res := [] ; for s from k*(k+1)/2 to sumax do c := combinat[composition](s, k) ; for j from 1 to nops(c) do isord := true ; for i from 2 to nops(op(j, c)) do if op(i, op(j, c))<= op(i-1, op(j, c)) then isord := false ; fi ; od ; if isord then res := [op(res), op(j, c)] ; fi ; od ; od ; RETURN(res) ; end: qm := proc(gfpart, n) local f, i ; f := q^add(op(i, gfpart), i=1..nops(gfpart)) ; for i from 1 to nops(gfpart) do f := taylor(f/(1+q^op(i, gfpart)), q=0, n+1) ; od ; RETURN(f) ; end: A060186 := proc(n) local k, ms, gf, gfpart, i ; k := 3 ; ms := mufact(k, n) ; gf := 0; for i from 1 to nops(ms) do gfpart := op(i, ms) ; gf := taylor(gf+qm(gfpart, n), q=0, n+1) ; od ; RETURN(gf) ; end: nmax := 60 : a := A060186(nmax) : for n from 6 to nmax do printf("%d, ", coeftayl(a, q=0, n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2007

Sequence in context: A050340 A021955 A055191 this_sequence A122002 A073226 A021198

Adjacent sequences: A060183 A060184 A060185 this_sequence A060187 A060188 A060189

easy,more,sign

N. J. A. Sloane (njas(AT)research.att.com), Mar 19 2001

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2007