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A143229 a(n) = A000041(n) * A000070(n). 2

%I #5 Nov 04 2016 17:35:13

%S 1,2,8,21,60,133,330,675,1474,2910,5838,10920,20944,37673,68580,

%T 120384,211365,359964,614845,1022630,1701678,2776752,4517016,7232565,

%U 11557350,18201568,28579152,44373420,68634280,105109125,160436916,242692582,365853180,547346709

%N a(n) = A000041(n) * A000070(n).

%F a(n) = A000041(n) * A000070(n), where A000041 = the number of partitions of n and A000070 = partial sums of A000041. Equals row sums of triangle A143228.

%F a(n) ~ exp(2*sqrt(2*n/3)*Pi)/(8*sqrt(6)*Pi*n^(3/2)) * (1 + (5*Pi/(12*sqrt(6)) - sqrt(3/2)/Pi)/sqrt(n) + (13*Pi^2/1728 - 19/48)/n). - _Vaclav Kotesovec_, Nov 04 2016

%e a(4) = 60 = A000041(4) * A000070(4) = 5 *12.

%e a(4) = 60 = sum of row 4 terms of row 4 in triangle A143228: (5 + 5 + 10 + 15 + 25).

%Y Cf. A143228, A000041, A000070.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Jul 31 2008

%E More terms from _Vaclav Kotesovec_, Nov 04 2016

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Last modified July 21 21:26 EDT 2024. Contains 374475 sequences. (Running on oeis4.)