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 A255180 Number of partitions of n in which two summands (of each size) are designated. 1
 1, 0, 1, 3, 7, 10, 20, 24, 45, 61, 103, 140, 246, 325, 517, 728, 1086, 1472, 2184, 2918, 4197, 5638, 7875, 10497, 14625, 19272, 26354, 34804, 46992, 61490, 82471, 107163, 142128, 184141, 241701, 311282, 406164, 519755, 672726, 858110, 1102872 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{n>=1} 1 + x^(2*n)/(1 - x^n)^3. EXAMPLE a(4)=7. In order to designate two summands of each size, the multiplicity of each summand must be at least two. For n=4 we consider only the partitions 2+2 and 1+1+1+1. In the first case there is 1 way and in the second case there are 6 ways. 1 + 6 = 7. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+add(b(n-i*j, i-1)*binomial(j, 2), j=2..n/i))) end: a:= n-> b(n\$2): seq(a(n), n=0..50); # Alois P. Heinz, Mar 19 2015 MATHEMATICA nn = 40; CoefficientList[Series[Product[1 + x^(2 n)/(1 - x^n)^3, {n, 1, nn}], {x, 0, nn}], x] CROSSREFS Cf. A077285, A070933 (where any number of summands of any size are designated). Sequence in context: A000223 A366044 A031328 * A053159 A345891 A279912 Adjacent sequences: A255177 A255178 A255179 * A255181 A255182 A255183 KEYWORD nonn AUTHOR Geoffrey Critzer, Mar 19 2015 STATUS approved

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Last modified September 18 14:24 EDT 2024. Contains 376000 sequences. (Running on oeis4.)