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A268348 Number of partitions of (5, n) into a sum of distinct pairs. 3
3, 10, 21, 42, 74, 123, 197, 303, 452, 659, 943, 1323, 1830, 2496, 3363, 4485, 5922, 7748, 10058, 12958, 16578, 21077, 26637, 33476, 41855, 52077, 64496, 79536, 97683, 119505, 145671, 176948, 214225, 258542, 311085, 373227, 446553, 532873, 634265, 753118 (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^(5/4) * n^(7/4) * exp(Pi*sqrt(n/3)) / (5*Pi^5).

MATHEMATICA

max=50; col=5; 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-François Alcover *)

nmax = 50; CoefficientList[Series[((3 + 4*x + x^2 - 4*x^4 - 5*x^5 - 4*x^6 + 2*x^8 + 3*x^9 + 3*x^10 - x^12 - 2*x^13 + x^14) / ((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^5)))*Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Column 5 of A054242.

Sequence in context: A294365 A210980 A207380 * A117495 A007687 A192033

Adjacent sequences:  A268345 A268346 A268347 * A268349 A268350 A268351

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 02 2016

STATUS

approved

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)