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Search: id:A136578
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| A136578 |
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G.f.: A(x) = Sum_{n>=0} log( (1 + 2^n*x)*(1 + 3^n*x) )^n / n!. |
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+0
1
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| 1, 5, 78, 6527, 3450452, 12594729052, 338284182093366, 70004091118158663618, 115159273597941035104859580, 1536760523930850376685165570432060, 168534058834325412618424268506407590697776
(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*3^(n-k), k) * C(2^k*3^(n-k), n-k).
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EXAMPLE
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G.f. A(x) = 1 + 5*x + 78*x^2 + 6527*x^3 + 3450452*x^4 +...
A(x) = 1 + log((1+2x)(1+3x)) + log((1+4x)(1+9x))^2/2! + log((1+8x)(1+27x))^3/3! +...
More generally: if Sum_{n>=0} (1+p^n*x)^b*(1+q^n*x)^d * log((1+p^n*x)*(1+q^n*x))^n /n! = Sum_{n>=0} a(n)*x^n then a(n) = Sum_{k=0..n} C(p^k*q^(n-k)+b, k) * C(p^k*q^(n-k)+d, n-k).
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PROGRAM
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(PARI) {a(n)=polcoeff(sum(i=0, n, log((1+2^i*x)*(1+3^i*x)+x*O(x^n))^i/i!), n)}
(PARI) {a(n)=sum(k=0, n, binomial(2^k*3^(n-k), k)*binomial(2^k*3^(n-k), n-k))}
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CROSSREFS
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Adjacent sequences: A136575 A136576 A136577 this_sequence A136579 A136580 A136581
Sequence in context: A009485 A015056 A015973 this_sequence A057186 A106939 A142114
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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 08 2008, Jan 23 2008
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