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Search: id:A117409
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| A117409 |
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Number of partitions of n into odd parts in which the largest part occurs only once. |
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+0
2
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| 1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 142, 165, 192, 222, 256, 296, 340, 390, 448, 512, 585, 668, 760, 864, 982, 1113, 1260, 1426, 1610, 1816, 2048, 2304, 2590, 2910, 3264, 3658, 4097, 4582, 5120, 5718, 6378
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n)=A117408(n,1).
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FORMULA
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G.f.: Sum_{k>0} x^(2k-1)/(Product_{0<i<k} 1-x^(2i-1)).
a(n)=A000009(n-2), n>2. - Michael Somos May 28 2006
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EXAMPLE
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a(9)=5 because we have [9],[7,1,1],[5,3,1],[5,1,1,1,1] and [3,1,1,1,1,1,1].
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MAPLE
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f:=sum(x^(2*k-1)/product(1-x^(2*i-1), i=1..k-1), k=1..40): fser:=series(f, x=0, 70): seq(coeff(fser, x^n), n=1..65);
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PROGRAM
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(PARI) {a(n)=if(n<3, n==1, n-=2; polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n)), n))} /* Michael Somos May 28 2006 */
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CROSSREFS
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Cf. A117408.
Sequence in context: A034320 A000009 A081360 this_sequence A092833 A100926 A157046
Adjacent sequences: A117406 A117407 A117408 this_sequence A117410 A117411 A117412
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
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