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A014160 Apply partial sum operator thrice to partition numbers. 4
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

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.

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

N. J. A. Sloane.

STATUS

approved

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Last modified August 20 00:52 EDT 2018. Contains 313902 sequences. (Running on oeis4.)