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

1, 2, 8, 21, 60, 133, 330, 675, 1474, 2910, 5838, 10920, 20944, 37673, 68580, 120384, 211365, 359964, 614845, 1022630, 1701678, 2776752, 4517016, 7232565, 11557350, 18201568, 28579152, 44373420, 68634280, 105109125, 160436916, 242692582, 365853180, 547346709

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Formula

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.

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

Example

a(4) = 60 = A000041(4) * A000070(4) = 5 *12.
a(4) = 60 = sum of row 4 terms of row 4 in triangle A143228: (5 + 5 + 10 + 15 + 25).

Crossrefs

Cf. A143228, A000041, A000070.

Sequence in context: A216893 A264245 A123044 * A123285 A143212 A316270

Adjacent sequences: A143226 A143227 A143228 * A143230 A143231 A143232

Keyword

nonn

Author

Gary W. Adamson, Jul 31 2008

Extensions

More terms from Vaclav Kotesovec, Nov 04 2016

Status

approved