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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

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Last modified October 16 08:03 EDT 2018. Contains 316259 sequences. (Running on oeis4.)