This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A115584 Number of partitions of n in which each part k occurs more than k times. 4
 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 4, 3, 6, 4, 7, 7, 8, 8, 12, 9, 15, 14, 17, 18, 24, 21, 29, 29, 35, 35, 46, 42, 56, 54, 65, 67, 81, 77, 98, 95, 115, 114, 139, 135, 164, 165, 190, 195, 230, 225, 272, 271, 313, 321, 370, 374, 433, 441, 501, 514, 589, 592, 681, 698, 778, 809, 907 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{k>=1} (1-x^k+x^(k*(k+1)))/(1-x^k). EXAMPLE a(2) = 1 because we have [1,1]; a(10) = 4 because we have [2,2,2,2,2], [2,2,2,2,1,1], [2,2,2,1,1,1,1] and [1^10]. MAPLE g:=product((1-x^k+x^(k*(k+1)))/(1-x^k), k=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=0..70); # Emeric Deutsch, Mar 12 2006 # second Maple program: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       b(n, i-1) +add(b(n-i*j, i-1), j=i+1..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..80);  # Alois P. Heinz, Feb 09 2017 MATHEMATICA CoefficientList[ Series[ Product[(1 - x^k + x^(k(k + 1)))/(1 - x^k), {k, 14}], {x, 0, 66}], x] - Robert G. Wilson v CROSSREFS Cf. A117144, A052335, A087153. Sequence in context: A230560 A265253 A161227 * A058742 A029140 A008584 Adjacent sequences:  A115581 A115582 A115583 * A115585 A115586 A115587 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Mar 09 2006 EXTENSIONS More terms from Robert G. Wilson v and Emeric Deutsch, Mar 12 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 January 19 21:52 EST 2019. Contains 319310 sequences. (Running on oeis4.)