This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A116856 Triangle read by rows: T(n,k) is the number of partitions of n into odd parts such that the smallest part is k (n>=1, k>=1). 2
 1, 1, 1, 0, 1, 2, 2, 0, 0, 0, 1, 3, 0, 1, 4, 0, 0, 0, 0, 0, 1, 5, 0, 1, 6, 0, 1, 0, 0, 0, 0, 0, 1, 8, 0, 1, 0, 1, 10, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 12, 0, 2, 0, 1, 15, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 18, 0, 2, 0, 1, 0, 1, 22, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 27, 0, 3, 0, 1, 0, 1, 32, 0, 4, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Row 2n-1 has 2n-1 terms; row 4n+2 has 2n+1 terms; row 4n has 2n-1 terms. Row sums yield A000009. T(n,2k)=0. Sum(k*T(n,k),k>=1)=A092314(n) LINKS FORMULA G.f.=sum(t^(2j-1)*x^(2j-1)/product(1-x^(2i-1), i=j..infinity), j=1..infinity). EXAMPLE T(12,3)=2 because we have [9,3] and [3,3,3,3]. Triangle starts: 1; 1; 1,0,1; 2; 2,0,0,0,1; 3,0,1; 4,0,0,0,0,0,1 MAPLE g:=sum(t^(2*j-1)*x^(2*j-1)/product(1-x^(2*i-1), i=j..20), j=1..30): gser:=simplify(series(g, x=0, 20)): for n from 1 to 17 do P[n]:=sort(coeff(gser, x^n)) od: d:=proc(n) if n mod 2 = 1 then n elif n mod 4 = 2 then n/2 else n/2-1 fi end: for n from 1 to 17 do seq(coeff(P[n], t^j), j=1..d(n)) od; # yields sequence in triangular form; d(n) is the degree of the polynomial P[n] CROSSREFS Cf. A000009, A092314, A116799. Sequence in context: A131018 A300067 A035395 * A140344 A279479 A318584 Adjacent sequences:  A116853 A116854 A116855 * A116857 A116858 A116859 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Feb 24 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)