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Search: id:A136554
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| A136554 |
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G.f.: A(x) = Sum_{n>=0} log( (1 + x)*(1 + 2^n*x) )^n / n!. |
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+0
1
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| 1, 3, 10, 82, 2304, 232088, 81639942, 99425060368, 421915147527984, 6313762292901492960, 337457827116687464134048, 65175276571204939272971781496, 45944813538624773942727094008288680
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = Sum_{k=0..n} C(2^k, k)*C(2^k, n-k). G.f.: A(x) = Sum_{n>=0} C(2^n,n)*x^n*(1+x)^(2^n).
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 10*x^2 + 82*x^3 + 2304*x^4 + 232088*x^5 +...;
A(x) = 1 + log((1+x)*(1+2*x)) + log((1+x)*(1+4*x))^2/2! + log((1+x)*(1+8*x))^3/3! + log((1+x)*(1+16*x))^4/4! +...
Surprisingly, this sum yields a series in x with only integer coefficients.
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PROGRAM
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(PARI) {a(n)=polcoeff(sum(i=0, n, log((1+x)*(1+2^i*x)+x*O(x^n))^i/i!), n)}
(PARI) {a(n)=sum(k=0, n, binomial(2^k, k)*binomial(2^k, n-k))}
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CROSSREFS
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Adjacent sequences: A136551 A136552 A136553 this_sequence A136555 A136556 A136557
Sequence in context: A086846 A082245 A027159 this_sequence A136505 A006311 A034792
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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), Jan 06 2008, Jan 07 2008
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