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Search: id:A118192
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| A118192 |
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Antidiagonal sums of triangle A118190: a(n) = Sum_{k=0..[n/2]} (5^k)^(n-2*k) for n>=0. |
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+0
3
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| 1, 1, 2, 6, 27, 151, 1252, 18876, 421877, 11797501, 489062502, 36867190626, 4119892578127, 576049853531251, 119400024902343752, 45003894807128984376, 25145828723919677734377, 17579646409034759521875001
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = Sum_{n>=0} x^n/(1-5^n*x^2). a(2*n) = Sum_{k=0..n} (5^k)^(2(n-k)); a(2*n+1) = Sum_{k=0..n} (5^k)^(2(n-k)+1).
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EXAMPLE
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A(x) = 1/(1-x^2) + x/(1-5x^2) + x^2/(1-25x^2) + x^3/(1-125x^2) +...
= 1 + x + 2*x^2 + 6*x^3 + 27*x^4 + 151*x^5 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n\2, (5^k)^(n-2*k) )
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CROSSREFS
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Cf. A118190 (triangle), A118191 (row sums).
Sequence in context: A030967 A030858 A030932 this_sequence A058133 A009308 A032186
Adjacent sequences: A118189 A118190 A118191 this_sequence A118193 A118194 A118195
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2006
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