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Search: id:A117457
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| A117457 |
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Number of parts in all partitions of n in which every integer from the smallest part to the largest part occurs as a part. |
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+0
2
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| 1, 3, 6, 10, 15, 24, 32, 45, 63, 82, 107, 144, 179, 228, 296, 362, 450, 564, 684, 839, 1029, 1232, 1487, 1799, 2141, 2546, 3044, 3589, 4237, 5015, 5863, 6869, 8051, 9361, 10904, 12677, 14657, 16948, 19595, 22552, 25927, 29812, 34130, 39066, 44703
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=sum(A117456(n,k),k=1..n).
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FORMULA
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G.f.=sum(jx^j*product(1+x^i, i=1..j-1)/(1-x^j), j=1..infinity) (obtained by taking the derivative with respect to t of the g.f. G(t,x) of A117456 and setting t=1).
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EXAMPLE
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a(5)=15 because in the 5 (=A034296(5)) partitions in which every integer from the smallest to the largest part occurs, namely [5],[3,2],[2,2,1],[2,1,1,1], and [1,1,1,1,1], the total number of parts is 1+2+3+4+5=15.
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MAPLE
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g:=sum(j*x^j*product(1+x^i, i=1..j-1)/(1-x^j), j=1..60): gser:=series(g, x=0, 55): seq(coeff(gser, x^n), n=1..50);
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CROSSREFS
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Cf. A034296, A117456.
Sequence in context: A063542 A122554 A111734 this_sequence A024674 A026104 A058576
Adjacent sequences: A117454 A117455 A117456 this_sequence A117458 A117459 A117460
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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 18 2006
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