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 A202139 Expansion of e.g.f. log(1/(1-arctanh(x))). 8
 0, 1, 1, 4, 14, 88, 544, 4688, 41712, 459520, 5333376, 71876352, 1027670016, 16428530688, 278818065408, 5167215464448, 101437811718144, 2140879726411776, 47698275298050048, 1130276555155243008, 28167446673847812096, 740796870212763254784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..431 FORMULA a(n) = n! * Sum_{m=1..n} (m-1)! * Sum_{k=0..n-m} Stirling1(k+m,m) * 2^k * binomial(n-1,k+m-1)/(k+m)!. E.g.f.: log(2) - log(2 + log((1-x)/(1+x))). - Arkadiusz Wesolowski, Feb 19 2013 a(n) ~ n! * ((exp(2)+1)/(exp(2)-1))^n/n. - Vaclav Kotesovec, Jun 13 2013 a(0) = 0; a(n) = (n mod 2) * (n-1)! + Sum_{k=1..floor(n/2)} (2*k-2)! * binomial(n-1,2*k-1) * a(n-2*k+1). - Seiichi Manyama, Apr 30 2022 MATHEMATICA With[{nn=30}, CoefficientList[Series[Log[1/(1-ArcTanh[x])], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 10 2022 *) PROG (Maxima) a(n):=n!*sum(((m-1)!*sum((stirling1(k+m, m)*2^k*binomial(n-1, k+m-1))/(k+m)!, k, 0, n-m)), m, 1, n); (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; for(i=1, n, v[i+1]=(i%2)*(i-1)!+sum(j=1, i\2, (2*j-2)!*binomial(i-1, 2*j-1)*v[i-2*j+2])); v; \\ Seiichi Manyama, Apr 30 2022 CROSSREFS Cf. A003704, A226968. Sequence in context: A339193 A352289 A330465 * A331637 A340024 A190481 Adjacent sequences: A202136 A202137 A202138 * A202140 A202141 A202142 KEYWORD nonn AUTHOR Vladimir Kruchinin, Dec 12 2011 EXTENSIONS Zero prepended by Harvey P. Dale, Sep 10 2022 STATUS approved

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Last modified August 6 22:39 EDT 2024. Contains 375001 sequences. (Running on oeis4.)