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 A026803 Number of partitions of n in which the least part is 10. 18
 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 27, 29, 34, 37, 43, 47, 54, 59, 68, 74, 85, 93, 106, 116, 132, 145, 164, 180, 203, 223, 252, 276, 310, 341, 382, 420, 470, 516, 576, 633, 706, 775, 863 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,30 COMMENTS In general, if g>=1 and g.f. = x^g * Product_{m>=g} 1/(1-x^m), then a(n,g) ~ Pi^(g-1) * (g-1)! * exp(Pi*sqrt(2*n/3)) / (2^((g+3)/2) * 3^(g/2) * n^((g+1)/2)) ~ p(n) * Pi^(g-1) * (g-1)! / (6*n)^((g-1)/2), where p(n) is the partition function A000041(n). - Vaclav Kotesovec, Jun 02 2018 LINKS FORMULA G.f.: x^10 * Product 1/(1-x^m); m=10..inf. a(n) ~ exp(Pi*sqrt(2*n/3)) * 35*sqrt(2)*Pi^9 / (3*n^(11/2)). - Vaclav Kotesovec, Jun 02 2018 CROSSREFS Not necessarily connected 2-regular graphs with girth at least g [partitions into parts >= g]: A026807 (triangle); chosen g: A000041 (g=1 -- multigraphs with loops allowed), A002865 (g=2 -- multigraphs with loops forbidden), A008483 (g=3), A008484 (g=4), A185325(g=5), A185326 (g=6), A185327 (g=7), A185328 (g=8), A185329 (g=9). Not necessarily connected 2-regular graphs with girth exactly g [partitions with smallest part g]: A026794 (triangle); chosen g: A002865 (g=2 -- multigraphs with at least one pair of parallel edges, but loops forbidden), A026796 (g=3), A026797 (g=4), A026798 (g=5), A026799 (g=6), A026800 (g=7), A026801 (g=8), A026802 (g=9), A026803 (g=10). Sequence in context: A264593 A026828 A025153 * A286041 A027192 A194255 Adjacent sequences:  A026800 A026801 A026802 * A026804 A026805 A026806 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Arlin Anderson (starship1(AT)gmail.com), Apr 12 2001 STATUS approved

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)