This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050343 Number of partitions of n into distinct parts with 2 levels of parentheses. 12
 1, 1, 1, 4, 7, 14, 29, 57, 110, 217, 417, 794, 1513, 2860, 5373, 10063, 18740, 34750, 64221, 118199, 216775, 396297, 722136, 1311888, 2376575, 4293407, 7735941, 13903985, 24929763, 44595606, 79598328, 141770576, 251984463, 446991405, 791391545, 1398551523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, Transforms FORMULA Weigh transform of A050342. EXAMPLE 4 = ((4)) = ((3))+((1)) = ((3)+(1)) = ((3+1)) = ((2+1))+((1)) = ((2+1)+(1)). MAPLE g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       g(n, i-1)+`if`(i>n, 0, g(n-i, i-1))))     end: h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(binomial(g(i, i), j)*h(n-i*j, i-1), j=0..n/i)))     end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(binomial(h(i, i), j)*b(n-i*j, i-1), j=0..n/i)))     end: a:= n-> b(n, n): seq(a(n), n=0..50); # Alois P. Heinz, May 19 2013 MATHEMATICA g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, g[n, i-1] + If[i>n, 0, g[n-i, i-1]]]] ; h[n_, i_] := h[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*h[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[ Binomial[ h[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 17 2015, after Alois P. Heinz *) CROSSREFS Cf. A050342-A050350. Sequence in context: A094968 A049946 A076975 * A245002 A199628 A049945 Adjacent sequences:  A050340 A050341 A050342 * A050344 A050345 A050346 KEYWORD nonn AUTHOR Christian G. Bower, Oct 15 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 December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)