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 A014160 Apply partial sum operator thrice to partition numbers. 5
 1, 4, 11, 25, 51, 96, 171, 291, 478, 762, 1185, 1803, 2693, 3956, 5727, 8182, 11552, 16134, 22313, 30579, 41559, 56045, 75039, 99796, 131891, 173282, 226405, 294270, 380595, 489945, 627924, 801374, 1018644 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A014160 convolved with A010815 = A000217, the triangular numbers. - Gary W. Adamson, Nov 09 2008 Unordered partitions of n into parts where the part 1 comes in 4 colors. - Peter Bala, Dec 23 2013 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA From Peter Bala, Dec 23 2013: (Start) O.g.f.: 1/(1 - x)^3 * product {k >= 1} 1/(1 - x^k). a(n-1) + a(n-2) = sum {parts k in all partitions of n} J_2(k), where J_2(n) is the Jordan totient function A007434(n). (End) a(n) ~ 3*sqrt(n) * exp(Pi*sqrt(2*n/3)) / (sqrt(2)*Pi^3). - Vaclav Kotesovec, Oct 30 2015 a(n) = Sum_{k=0..n} A014153(k). - Sean A. Irvine, Oct 14 2018 MATHEMATICA nmax = 50; CoefficientList[Series[1/((1-x)^3 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *) CROSSREFS Cf. A000041, A000070, A014153. Cf. A010815, A000217. - Gary W. Adamson, Nov 09 2008 Column k=4 of A292508. Sequence in context: A011851 A193912 A136395 * A014162 A014169 A113684 Adjacent sequences:  A014157 A014158 A014159 * A014161 A014162 A014163 KEYWORD nonn AUTHOR STATUS approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)