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A218004
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Number of equivalence classes of compositions of n where two compositions a,b are considered equivalent if the summands of a can be permuted into the summands of b with an even number of transpositions.
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0
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1, 1, 2, 4, 6, 9, 14, 19, 27, 37, 51, 67, 91, 118, 156, 202, 262, 334, 430, 543, 690, 867, 1090, 1358, 1696, 2099, 2600, 3201, 3939, 4820, 5899, 7181, 8738, 10590, 12821, 15467, 18644, 22396, 26878, 32166, 38450, 45842, 54599, 64870, 76990, 91181, 107861, 127343, 150182, 176788, 207883
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OFFSET
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0,3
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COMMENTS
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a(n) = A000041(n) + A000009(n) - 1 where A000041 is the partition numbers and A000009 is the number of partitions into distinct parts.
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LINKS
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Table of n, a(n) for n=0..50.
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EXAMPLE
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a(4) = 6 because the 6 classes can be represented by: 4, 3+1, 1+3, 2+2, 2+1+1, 1+1+1+1.
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MATHEMATICA
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nn=50; p=CoefficientList[Series[Product[1/(1-x^i), {i, 1, nn}], {x, 0, nn}], x]; d= CoefficientList[Series[Sum[Product[x^i/(1-x^i), {i, 1, k}], {k, 0, nn}], {x, 0, nn}], x]; p+d-1
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CROSSREFS
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Cf. A008965, A091696.
Sequence in context: A067588 A003402 A328863 * A034748 A069916 A153140
Adjacent sequences: A218001 A218002 A218003 * A218005 A218006 A218007
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KEYWORD
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nonn
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AUTHOR
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Geoffrey Critzer, Oct 17 2012
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STATUS
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approved
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