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A158843
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G.f.: A(x) = exp( Sum_{n>=1} A001333(n)^n * 2^n*x^n/n ).
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1, 2, 20, 952, 336112, 742166496, 10043945021760, 814531629739559808, 393150002983518264270592, 1123538097532735360702239462912, 18948231465474675384343860006353603584
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Compare to g.f.: exp( Sum_{n>=1} 2*A001333(n)*x^n/n ) = 1/(1-2*x-x^2), which is the g.f. of the Pell numbers A000129 (with offset), where A001333(n) = A000129(n+1) - A000129(n).
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EXAMPLE
| G.f.: A(x) = 1 + 2*x + 20*x^2 + 952*x^3 + 336112*x^4 + 742166496*x^5 +...
log(A(x)) = 2*x + 6^2*x^2/2 + 14^3*x^3/3 + 34^4*x^4/4 + 82^5*x^5/5 +...
log(G(x)) = 2*x + 6*x^2/2 + 14*x^3/3 + 34*x^4/4 + 82*x^5/5 +...
G(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 29*x^4 + 70*x^5 + 169*x^6 +... (A000129).
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PROG
| (PARI) {a(n)=local(LD=Vec(2*(1+x)/(1-2*x-x^2 +x*O(x^n)))); polcoeff(exp(sum(m=1, n, LD[m]^m*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
| Cf. A000129, A001333.
Sequence in context: A013148 A006547 A135757 * A008793 A015192 A012790
Adjacent sequences: A158840 A158841 A158842 * A158844 A158845 A158846
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 09 2009
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