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 A237998 Number of partitions of 2^n into parts that are at most n. 11
 0, 1, 3, 10, 64, 831, 26207, 2239706, 567852809, 454241403975, 1192075219982204, 10510218491798860052, 315981966712495811700951, 32726459268483342710907384794, 11771239570056489326716955796095261, 14808470136486015545654676685321653888199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..62 A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz) (arXiv:1108.4391 [math.CO]) FORMULA a(n) = [x^(2^n)] Product_{j=1..n} 1/(1-x^j). a(n) ~ 2^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015 EXAMPLE a(1) = 1: 11. a(2) = 3: 22, 211, 1111. a(3) = 10: 332, 2222, 3221, 3311, 22211, 32111, 221111, 311111, 2111111, 11111111. MATHEMATICA a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, 2^n}]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 03 2018 *) CROSSREFS Column k=2 of A238010. Cf. A236810, A237512, A237999, A238000, A238001, A258672. Sequence in context: A042705 A041014 A367641 * A167939 A352766 A206724 Adjacent sequences: A237995 A237996 A237997 * A237999 A238000 A238001 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 16 2014 STATUS approved

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Last modified September 18 20:23 EDT 2024. Contains 376002 sequences. (Running on oeis4.)