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Search: id:A105219
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| A105219 |
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Let b(n) denote the squares, A000290: a(n) = Sum{k=0..n}C(n,k)^2*(n-k)!*b(k). |
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+0
1
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| 0, 1, 8, 63, 544, 5225, 55656, 653023, 8379008, 116780049, 1757211400, 28394129951, 490371506208, 9013522796473, 175679564492264, 3618800515187775, 78547755741723136, 1791704327280481313
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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If E.g.f. of b(n) is E(x), and a(n) =Sum{k=0..n}C(n,k)^2*(n-k)!*b(k), then E.g.f. of a(n) is E(x/(1-x))/(1-x). (Thanks to Vladeta Jovovic for help.)
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FORMULA
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E.g.f. = (x/(1-x)^2+x^2/(1-x)^3)*exp(x/(1-x))
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EXAMPLE
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b(n) = 0,1,4,9,16,25,36,49,64,...
a(3) = C(3,0)^2*3!*b(0)+C(3,1)^2*2!*b(1)+C(3,2)^2*1!*b(2)+C(3,3)^2*0!*b(3) = 1*6*0+9*2*1+9*1*4+1*1*9 = 0+18+36+9 = 63
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MAPLE
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for n from 0 to 30 do b[n]:=n^2 od: > seq(sum('binomial(n, k)^2*(n-k)!*b[k]', 'k'=0..n), n=0..30);
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CROSSREFS
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Cf. A000290.
Sequence in context: A085433 A081107 A001090 this_sequence A037205 A060071 A084096
Adjacent sequences: A105216 A105217 A105218 this_sequence A105220 A105221 A105222
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Apr 13 2005
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