This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005895 Weighted count of partitions with distinct parts. (Formerly M1337) 5
 1, 2, 5, 7, 12, 18, 26, 35, 50, 67, 88, 116, 149, 191, 245, 306, 381, 477, 585, 718, 880, 1067, 1288, 1555, 1863, 2226, 2656, 3151, 3726, 4406, 5180, 6077, 7124, 8316, 9691, 11278, 13080, 15146, 17517, 20204, 23264, 26759, 30705, 35182, 40274, 46000, 52473, 59795, 68018, 77279, 87711, 99395, 112508 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also sum of largest parts of all partitions of n into distinct parts. - Vladeta Jovovic, Feb 15 2004 REFERENCES Andrews, George E.; Ramanujan's "lost" notebook. V. Euler's partition identity. Adv. in Math. 61 (1986), no. 2, 156-164. S.-Y. Kang, Generalizations of Ramanujan's reciprocity theorem..., J. London Math. Soc., 75 (2007), 18-34. See Eq. (1.5) but beware errors. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA G.f.: sum(n>=0, S(q) - prod(k=1..n, 1+q^k) ), where S(q)=prod(k>=1, 1+q^k) (g.f. for A000009). G.f. sum(k>=0, (k+1)*x^(k+1) * prod(j=1..k, 1+x^j) ). [Joerg Arndt, Sep 17 2012] MAPLE M:=201; add( mul( (1+q^j), j=1..M) - mul( (1+q^j), j=1..n), n=0..M); # second Maple program: b:= proc(n, i) option remember; `if`(n>i*(i+1)/2, 0, `if`(       n=0, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, min(n-i, i-1)))))     end: a:= n-> add(j*b(n-j, min(n-j, j-1)), j=1..n): seq(a(n), n=1..80);  # Alois P. Heinz, Feb 03 2016 MATHEMATICA m = 46; f[q_] :=  Sum[ Product[ (1+q^j), {j, 1, m}] - Product[ (1+q^j), {j, 1, n}], {n, 0, m}]; CoefficientList[ f[q], q][[2 ;; m+1]] (* Jean-François Alcover, Apr 13 2012, after Maple *) PROG (PARI) N=66;  x='x+O('x^N); S=prod(k=1, N, 1+x^k); gf=sum(n=0, N, S-prod(k=1, n, 1+x^k)); /* alternative: Arndt's g.f.: */ /* gf=sum(k=0, N, (k+1)*x^(k+1) * prod(j=1, k, 1+x^j) ); */ Vec(gf) /* Joerg Arndt, Sep 17 2012 */ CROSSREFS Cf. A005896, A003406. Sequence in context: A023668 A023564 A173088 * A238661 A135525 A319142 Adjacent sequences:  A005892 A005893 A005894 * A005896 A005897 A005898 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 24 1999 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 23 16:45 EDT 2019. Contains 328373 sequences. (Running on oeis4.)