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 A092268 Total number of smallest parts in all partitions of n into odd parts. 16
 1, 2, 4, 5, 8, 12, 15, 20, 29, 36, 46, 61, 74, 95, 122, 145, 180, 224, 268, 328, 399, 474, 567, 682, 807, 955, 1136, 1330, 1564, 1842, 2140, 2499, 2914, 3375, 3917, 4533, 5220, 6014, 6929, 7942, 9102, 10430, 11898, 13582, 15489, 17600, 19999, 22706, 25719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..2500 FORMULA G.f.: Sum((x^(2*n-1)/(1-x^(2*n-1)))/Product((1-x^(2*k-1)), k=n..infinity), n=1..infinity). a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, Jul 07 2019 EXAMPLE Partitions of 6 into odd parts are: [1,1,1,1,1,1], [1,1,1,3], [3,3], [1,5]; thus a(6)=6+3+2+1=12. MATHEMATICA nmax = 50; Rest[CoefficientList[Series[Sum[(x^(2*n - 1)/(1 - x^(2*n - 1))) / Product[(1 - x^(2*k - 1)), {k, n, nmax}], {n, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 06 2019 *) CROSSREFS Cf. A092314, A092322, A092269, A092309, A092321, A092313, A092310, A092311. Cf. A067588. Sequence in context: A287346 A035001 A260386 * A335702 A069259 A102186 Adjacent sequences:  A092265 A092266 A092267 * A092269 A092270 A092271 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 16 2004 EXTENSIONS More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004 STATUS approved

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Last modified May 16 00:49 EDT 2021. Contains 343937 sequences. (Running on oeis4.)