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 A002759 Number of bipartite partitions of n white objects and 10 black ones. (Formerly M5278 N2295) 4
 42, 139, 392, 907, 1941, 3804, 7128, 12693, 21893, 36535, 59521, 94664, 147794, 226524, 342006, 508866, 747753, 1085635, 1559725, 2218272, 3126541, 4368724, 6056705, 8333955, 11388614, 15460291, 20859497, 27979454, 37324367, 49529018 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Number of ways to factor p^n*q^10 where p and q are distinct primes. a(n) = if n <= 10 then A054225(10,n) else A054225(n,10). - Reinhard Zumkeller, Nov 30 2011 REFERENCES M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 2. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..200 from Alois P. Heinz) M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956 (Annotated scanned pages from, plus a review) FORMULA a(n) ~ sqrt(3) * n^4 * exp(Pi*sqrt(2*n/3)) / (5600*Pi^10). - Vaclav Kotesovec, Feb 01 2016 MATHEMATICA p = 2; q = 3; b[n_, k_] := b[n, k] = If[n>k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d>k, 0, b[n/d, d]], {d, DeleteCases[Divisors[n], 1|n]}]]; a[n_] := b[p^n*q^10, p^n*q^10]; Table[a[n], {n, 0, 29}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *) nmax = 50; CoefficientList[Series[(42 + 55*x + 72*x^2 + 68*x^3 + 55*x^4 + 22*x^5 - 21*x^6 - 72*x^7 - 126*x^8 - 178*x^9 - 222*x^10 - 203*x^11 - 169*x^12 - 81*x^13 + 15*x^14 + 125*x^15 + 209*x^16 + 286*x^17 + 303*x^18 + 299*x^19 + 219*x^20 + 107*x^21 - 4*x^22 - 117*x^23 - 208*x^24 - 263*x^25 - 257*x^26 - 232*x^27 - 151*x^28 - 69*x^29 + 29*x^30 + 92*x^31 + 130*x^32 + 145*x^33 + 143*x^34 + 97*x^35 + 48*x^36 - 2*x^37 - 39*x^38 - 48*x^39 - 58*x^40 - 41*x^41 - 31*x^42 - 19*x^43 - 4*x^44 + 19*x^45 + 21*x^46 + 20*x^47 + 13*x^48 - 4*x^49 - 9*x^50 - 10*x^51 + 2*x^52 + 4*x^53 - x^54)/((1-x) * (1-x^2) * (1-x^3) * (1-x^4) * (1-x^5) * (1-x^6) * (1-x^7) * (1-x^8) * (1-x^9) * (1-x^10)) * Product[1/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 01 2016 *) CROSSREFS Column 10 of A054225. Cf. A005380. Sequence in context: A244102 A045088 A303860 * A330939 A044374 A044755 Adjacent sequences:  A002756 A002757 A002758 * A002760 A002761 A002762 KEYWORD nonn AUTHOR EXTENSIONS Edited by Christian G. Bower, Jan 08 2004 STATUS approved

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Last modified March 28 17:51 EDT 2020. Contains 333103 sequences. (Running on oeis4.)