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 A185062 Number of n-element subsets that can be chosen from {1,2,...,2*n^3} having element sum n^4. 1
 1, 1, 7, 351, 56217, 18878418, 11163952389, 10292468330630, 13703363417260677, 24932632800863823135, 59509756600504616529186, 180533923700628895521591343, 678854993880375551144618682344, 3100113915888360851262910882014885 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of partitions of n^4 into n distinct parts <= 2*n^3. LINKS EXAMPLE a(0) = 1: {}. a(1) = 1: {1}. a(2) = 7: {1,15}, {2,14}, {3,13}, {4,12}, {5,11}, {6,10}, {7,9}. MAPLE b:= proc(n, i, t) option remember; `if`(it*(2*i-t+1)/2, 0, `if`(n=0, 1, b(n, i-1, t) +`if`(n b(n^4, 2*n^3, n): seq(a(n), n=0..5); MATHEMATICA \$RecursionLimit = 10000; b[n_, i_, t_] := b[n, i, t] = If[i < t || n < t(t+1)/2 || n > t(2i - t + 1)/2, 0, If[n == 0, 1, b[n, i-1, t] + If[n < i, 0, b[n-i, i-1, t-1]]]]; a[n_] := b[n^4, 2 n^3, n]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 10}] (* Jean-François Alcover, Mar 05 2021, after Alois P. Heinz *) CROSSREFS Column k=3 of A185282. Cf. A202261, A186730, A204459. Sequence in context: A142669 A239717 A266876 * A067556 A082098 A057634 Adjacent sequences: A185059 A185060 A185061 * A185063 A185064 A185065 KEYWORD nonn AUTHOR Alois P. Heinz, Jan 22 2012 STATUS approved

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)