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Search: id:A117467
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| A117467 |
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The smallest part summed over all partitions of n in which every integer from the smallest part to the largest part occurs. |
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+0
3
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| 1, 3, 5, 8, 10, 15, 17, 22, 28, 32, 37, 49, 52, 60, 77, 83, 94, 116, 125, 146, 174, 187, 214, 257, 282, 315, 372, 410, 461, 544, 593, 669, 773, 851, 969, 1105, 1218, 1368, 1559, 1737, 1936, 2199, 2431, 2717, 3079, 3396, 3790, 4263, 4719, 5262, 5878, 6501, 7224
(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(k*A117466(n,k),k=1..n).
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FORMULA
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G.f.=sum(x^j*product(1+x^i, i=1..j-1)/(1-x^j)^2, j=1..infinity) (obtained by taking the derivative with respect to t of the g.f. G(t,x) of A117466 and setting t=1).
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EXAMPLE
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a(5)=10 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 sum of the smallest parts is 5+2+1+1+1=10.
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MAPLE
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g:=sum(x^j*product(1+x^i, i=1..j-1)/(1-x^j)^2, j=1..70): gser:=series(g, x=0, 65): seq(coeff(gser, x, n), n=1..60);
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CROSSREFS
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Cf. A117466.
Sequence in context: A088940 A088937 A123327 this_sequence A133097 A117176 A127700
Adjacent sequences: A117464 A117465 A117466 this_sequence A117468 A117469 A117470
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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 19 2006
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