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A268347 Number of partitions of (4, n) into a sum of distinct pairs. 3
2, 7, 14, 27, 46, 74, 116, 174, 254, 363, 510, 703, 957, 1285, 1706, 2244, 2924, 3777, 4844, 6168, 7802, 9813, 12272, 15267, 18902, 23295, 28584, 34935, 42532, 51592, 62369, 75150, 90265, 108102, 129094, 153743, 182627, 216395, 255792, 301672, 354994, 416851 (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^(3/4) * n^(5/4) * exp(Pi*sqrt(n/3)) / (2*Pi^4).

MATHEMATICA

max=50; col=4; 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 + 3*x - x^3 - 4*x^4 - 2*x^5 + x^6 + x^7 + 2*x^8 - x^9) / ((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)))*Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Column 4 of A054242.

Sequence in context: A225277 A014112 A227016 * A210728 A294533 A294541

Adjacent sequences:  A268344 A268345 A268346 * A268348 A268349 A268350

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 02 2016

STATUS

approved

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)