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 A206157 G.f.: exp( Sum_{n>=1} A206158(n)*x^n/n ), where A206158(n) = Sum_{k=0..n} binomial(n,k)^(2*k+1). 3
 1, 2, 7, 102, 6261, 2423430, 6686021554, 61335432894584, 2941073857435300366, 1190520035262419577871332, 1696475310227140760623646031573, 9980324833243234634513255755001535870, 565171444566758371735408026461987217216896790 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Logarithmic derivative yields A206158. LINKS EXAMPLE G.f.: A(x) = 1 + 2*x + 7*x^2 + 102*x^3 + 6261*x^4 + 2423430*x^5 +... where the logarithm of the g.f. begins: log(A(x)) = 2*x + 10*x^2/2 + 272*x^3/3 + 24226*x^4/4 + 12053252*x^5/5 + 40086916024*x^6/6 +...+ A206158(n)*x^n/n +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*sum(k=0, m, binomial(m, k)^(2*k+1))+x*O(x^n))), n)} for(n=0, 16, print1(a(n), ", ")) CROSSREFS Cf. A206158 (log), A184730, A206153, A206155, A206151. Sequence in context: A277434 A192342 A102598 * A102747 A122524 A229165 Adjacent sequences:  A206154 A206155 A206156 * A206158 A206159 A206160 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 04 2012 STATUS approved

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