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Search: id:A073157
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| 1, 2, 5, 18, 70, 293, 1283, 5808, 26960, 127628, 613814, 2990681, 14730713, 73229291, 366936231, 1851352820, 9397497758, 47957377934, 245903408244, 1266266092112, 6545667052320, 33954266444498, 176689391245146
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OFFSET
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0,2
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FORMULA
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Convolution yields sequence A073155 minus the 0-th term: A073155(n+1)=sum{k=0..n} a(k)* a(n-k).
G.f.: A(x) = (1 - sqrt(1 - 4x(1+x)^2))/(2x(1+x)) where A(x) = (1+x)*(1 + x*A(x)^2); G.f.: A(x) = (1+x)*C(x*(1+x)^2) where C(x) is the Catalan g.f. of A000108. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2008
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 5*x^2 + 18*x^3 + 70*x^4 + 293*x^5 + 1283*x^6 +...
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PROGRAM
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(PARI) {a(n)=local(A=1); for(i=0, n-1, A=(1+x)*(1+x*(A+x*O(x^n))^2)); polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2008
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CROSSREFS
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Cf. A073154, A073155, A073156, A073153.
Cf. A000108.
Sequence in context: A150025 A118814 A014271 this_sequence A141494 A045612 A103940
Adjacent sequences: A073154 A073155 A073156 this_sequence A073158 A073159 A073160
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 29 2002
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EXTENSIONS
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More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2008
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