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 A132684 a(n) = binomial(2^n + n + 1, n). 3
 1, 4, 21, 220, 5985, 501942, 143218999, 145944307080, 542150225230185, 7398714129087308170, 372134605932348010322571, 69146263065062394421802892300, 47589861944854471977019273909187085 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA 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!). - Paul D. Hanna, Feb 25 2009 a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016 EXAMPLE From Paul D. Hanna, 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) MATHEMATICA Table[Binomial[2^n+n+1, n], {n, 0, 20}] (* Harvey P. Dale, Nov 10 2011 *) PROG (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)} \\ Paul D. Hanna, Feb 25 2009 CROSSREFS Cf. A060690, A132683. Cf. A066384. - Paul D. Hanna, Feb 25 2009 Sequence in context: A041667 A286883 A217144 * A032074 A197662 A203218 Adjacent sequences:  A132681 A132682 A132683 * A132685 A132686 A132687 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 26 2007 STATUS approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)