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Search: id:A117469
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| A117469 |
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The largest 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
2
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| 1, 3, 6, 9, 13, 19, 24, 30, 42, 49, 61, 79, 92, 110, 144, 162, 195, 242, 278, 332, 405, 463, 546, 656, 759, 882, 1049, 1205, 1399, 1655, 1887, 2181, 2546, 2909, 3361, 3880, 4422, 5069, 5831, 6641, 7566, 8666, 9818, 11159, 12730, 14376, 16281, 18465, 20828
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OFFSET
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1,2
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COMMENT
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a(n)=Sum(k*A117468(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+(1-x^j)sum(x^i/(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 A117468 and setting t=1).
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EXAMPLE
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a(5)=13 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 largest parts is 5+3+2+2+1=13.
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MAPLE
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g:=sum(x^j*product(1+x^i, i=1..j-1)*(1+(1-x^j)*sum(x^i/(1+x^i), i=1..j-1))/(1-x^j)^2, j=1..70): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=1..55);
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CROSSREFS
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Cf. A117466, A117467, A117468.
Sequence in context: A002578 A059293 A129728 this_sequence A073359 A137041 A086838
Adjacent sequences: A117466 A117467 A117468 this_sequence A117470 A117471 A117472
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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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