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A202139 Expansion of e.g.f. log(1/(1-arctanh(x))). 8
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

1,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..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(1) = 1; 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

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)); v[1]=1; for(i=2, n, v[i]=(i%2)*(i-1)!+sum(j=1, i\2, (2*j-2)!*binomial(i-1, 2*j-1)*v[i-2*j+1])); 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

STATUS

approved

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Last modified May 24 21:08 EDT 2022. Contains 354043 sequences. (Running on oeis4.)