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A268346 Number of partitions of (3, n) into a sum of distinct pairs. 3
2, 5, 9, 17, 27, 42, 64, 93, 132, 185, 254, 343, 459, 605, 790, 1024, 1314, 1673, 2118, 2661, 3324, 4132, 5107, 6282, 7695, 9383, 11396, 13792, 16629, 19982, 23938, 28586, 34037, 40420, 47868, 56546, 66640, 78348, 91908, 107589, 125680, 146522, 170499, 198027 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ 3^(1/4) * n^(3/4) * exp(Pi*sqrt(n/3)) / Pi^3.

MATHEMATICA

max=50; col=3; s1=Series[Product[(1+x^(n-k)*y^k), {n, 1, max+2}, {k, 0, n}], {y, 0, col}]//Normal; s2=Series[s1, {x, 0, max+1}]; a[n_]:=SeriesCoefficient[s2, {x, 0, n}, {y, 0, col}]; Table[a[n], {n, 0, max}] (* after Jean-Fran├žois Alcover *)

nmax = 50; CoefficientList[Series[((2 + x - x^2 - x^3 - x^4 + x^5) / ((1 - x)*(1 - x^2)*(1 - x^3))) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Column 3 of A054242.

Sequence in context: A167887 A023603 A062492 * A165271 A139672 A093694

Adjacent sequences:  A268343 A268344 A268345 * A268347 A268348 A268349

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 02 2016

STATUS

approved

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Last modified February 22 12:00 EST 2018. Contains 299452 sequences. (Running on oeis4.)