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A268345 Number of partitions of (2, n) into a sum of distinct pairs. 3
1, 3, 5, 9, 14, 21, 31, 44, 61, 83, 112, 148, 194, 251, 322, 410, 518, 649, 809, 1002, 1234, 1513, 1846, 2242, 2712, 3268, 3923, 4694, 5598, 6655, 7889, 9326, 10994, 12929, 15167, 17751, 20730, 24157, 28092, 32605, 37771, 43675, 50414, 58094, 66833, 76767 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ 3^(3/4) * n^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi^2).

MATHEMATICA

max=50; col=2; 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[(1 + x - x^2)/((1 - x)*(1 - x^2)) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Column 2 of A054242.

Sequence in context: A310040 A215369 A053618 * A267047 A032801 A033818

Adjacent sequences:  A268342 A268343 A268344 * A268346 A268347 A268348

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 02 2016

STATUS

approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)