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A078054
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Expansion of (1-x)/(1+2*x-2*x^2+x^3).
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0
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1, -3, 8, -23, 65, -184, 521, -1475, 4176, -11823, 33473, -94768, 268305, -759619, 2150616, -6088775, 17238401, -48804968, 138175513, -391199363, 1107554720, -3135683679, 8877676161, -25134274400, 71159584801, -201465394563, 570384233128, -1614858840183, 4571951541185
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=-2*a(n-1)+2*a(n-2)-a(n-3), a(0)=1, a(1)=-3.
a(n)=sum(m=1..n, sum(k=m..n, (sum(j=0..m, binomial(j,-3*m+k+2*j)*2^(-3*m+k+2*j)*(-1)^(j-m)*(-3)^(3*m-k-j)*binomial(m,j)))*binomial(n+m-k-1,m-1))), n>0, a(0)=1. [From Vladimir Kruchinin kru(AT)ie.tusur.ru, May 06 2011]
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PROG
| (Maxima)
a(n):=sum(sum((sum(binomial(j, -3*m+k+2*j)*2^(-3*m+k+2*j)*(-1)^(j-m)*(-3)^(3*m-k-j)*binomial(m, j), j, 0, m))*binomial(n+m-k-1, m-1), k, m, n), m, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, May 06 2011]
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CROSSREFS
| Sequence in context: A017930 A014398 A176880 * A018043 A147704 A116410
Adjacent sequences: A078051 A078052 A078053 * A078055 A078056 A078057
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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