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A118346
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Central terms of pendular triangle A118345.
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6
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1, 1, 5, 30, 201, 1445, 10900, 85128, 682505, 5585115, 46461437, 391743850, 3340361700, 28755475180, 249572076200, 2181469638880, 19186562661273, 169677521094215, 1507881643936015, 13458730170115778, 120599648894147185
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OFFSET
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0,3
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COMMENTS
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Also, g.f. A(x) = (1/x)*series_reversion of x/(1 + x*GF(A005572)), where GF(A005572) is the g.f. of A005572, which is the number of walks on cubic lattice starting and finishing on the xy plane and never going below it.
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: A=A(x) satisfies A = 1 - 2*x*A + 2*x*A^2 + x*A^3.
G.f.: A(x) = 1 + series_reversion[x/((1+x)*(1+4*x+x^2))].
G.f.: A(x) = (1/x)*series_reversion[ x*(1-2*x+sqrt((1-2*x)*(1-6*x)))/2/(1-2*x) ].
For n>0: a(n) = (1/n)*sum(binomial(n,j)*sum(binomial(j,i)*binomial(n-j,2*j-n-i-1)*5^(2*n-3*j+2*i+1),i=0..n-1), j=0..n). [Vladimir Kruchinin, Dec 26 2010]
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PROG
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(PARI) {a(n)=polcoeff(serreverse(x*(1-2*x+sqrt((1-2*x)*(1-6*x)+x*O(x^n)))/2/(1-2*x))/x, n)}
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CROSSREFS
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Cf. A118345, A118347, A118348, A118349.
Sequence in context: A196678 A128328 A245376 * A234422 A091927 A253076
Adjacent sequences: A118343 A118344 A118345 * A118347 A118348 A118349
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Apr 26 2006
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STATUS
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approved
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