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A132683
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a(n) = C(2^n + n, n).
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3
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1, 3, 15, 165, 4845, 435897, 131115985, 138432467745, 525783425977953, 7271150092378906305, 368539102493388126164865, 68777035446753808820521420545, 47450879627176629761462147774626305
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = [x^n] 1/(1-x)^(2^n + 1).
G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)*n!). [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
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EXAMPLE
| Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009: (Start)
G.f.: A(x) = 1 + 3*x + 15*x^2 + 165*x^3 + 4845*x^4 + 435897*x^5 +...
A(x) = 1/(1-x) - log(1-2x)/(1-2x) + log(1-4x)^2/((1-4x)*2!) - log(1-8x)^3/((1-8x)*3!) +-... (End)
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PROG
| (PARI) a(n)=binomial(2^n+n, n)
(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))*m!)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
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CROSSREFS
| Cf. A060690, A132684.
Cf. A066384. [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2009]
Sequence in context: A080696 A015013 A153280 * A059386 A077792 A153079
Adjacent sequences: A132680 A132681 A132682 * A132684 A132685 A132686
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 26 2007
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