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Search: id:A132684
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| A132684 |
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a(n) = C(2^n + n + 1, n). |
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+0
4
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| 1, 4, 21, 220, 5985, 501942, 143218999, 145944307080, 542150225230185, 7398714129087308170, 372134605932348010322571, 69146263065062394421802892300, 47589861944854471977019273909187085
(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) = [x^n] 1/(1-x)^(2^n + 2).
G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)^2*n!). [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
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EXAMPLE
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Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009: (Start)
G.f.: A(x) = 1 + 4*x + 21*x^2 + 220*x^3 + 5985*x^4 + 501942*x^5 +...
A(x) = 1/(1-x)^2 - log(1-2x)/(1-2x)^2 + log(1-4x)^2/((1-4x)^2*2!) - log(1-8x)^3/((1-8x)^2*3!) +-... (End)
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PROGRAM
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(PARI) a(n)=binomial(2^n+n+1, n)
(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))^2*m!)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
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CROSSREFS
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Cf. A060690, A132683.
Cf. A066384. [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
Sequence in context: A158258 A065527 A041667 this_sequence A032074 A006822 A165627
Adjacent sequences: A132681 A132682 A132683 this_sequence A132685 A132686 A132687
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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), Aug 26 2007
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