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A186730 Number of n-element subsets that can be chosen from {1,2,...,2*n^2} having element sum n^3. 2
1, 1, 3, 36, 785, 26404, 1235580, 74394425, 5503963083, 484133307457, 49427802479445, 5750543362215131, 751453252349649771, 109016775078856564392, 17391089152542558703435, 3026419470005398093836960, 570632810506646981058828349, 115900277419940965862120360831 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of partitions of n^3 into n distinct parts <= 2*n^2.

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

a(0) = 1: {}.

a(1) = 1: {1}.

a(2) = 3: {1,7}, {2,6}, {3,5}.

MAPLE

b:= proc(n, i, t) option remember;

      `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,

      `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))

    end:

a:= n-> b(n^3, 2*n^2, n):

seq(a(n), n=0..12);

CROSSREFS

Column k=2 of A185282.

Cf. A202261, A204459.

Sequence in context: A144758 A301582 A122220 * A224347 A227251 A326273

Adjacent sequences:  A186727 A186728 A186729 * A186731 A186732 A186733

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 21 2012

STATUS

approved

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Last modified January 23 10:50 EST 2020. Contains 331171 sequences. (Running on oeis4.)