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A189815
Expansion of e.g.f. log(1/(1-arcsin(x))).
7
1, 1, 3, 10, 53, 304, 2303, 18768, 185033, 1954176, 23756667, 308077056, 4457821821, 68513332224, 1150764459063, 20443736745984, 391167511473681, 7884821722497024, 169370797497060339, 3818539009013907456, 91013260219635394629, 2269047587255097753600, 59435772666287730632559
OFFSET
1,3
LINKS
FORMULA
a(n) = (n-1)!*Sum_{m=1..(n-1)} ((1+(-1)^(n-m))/2)*Sum_{k=1..(n-m)} (Sum_{j=1..k} binomial(k,j)*2^(1-j)*Sum_{i=0..floor(j/2)} (-1)^((n-m)/2-i-j)*binomial(j,i)*(j-2*i)^(n-m+j)/(n-m+j)!)*binomial(k+n-1,n-1)) + (n-1)!.
a(n) ~ (n-1)! / (sin(1))^n. - Vaclav Kotesovec, Nov 06 2014
MATHEMATICA
Rest[With[{nmax = 50}, CoefficientList[Series[Log[1/(1 - ArcSin[x])], {x, 0, nmax}], x]*Range[0, nmax]!]] (* G. C. Greubel, Jan 16 2018 *)
PROG
(Maxima) a(n):=(n-1)!*sum((1+(-1)^(n-m))/2*sum((sum(binomial(k, j)*2^(1-j)*sum((-1)^((n-m)/2-i-j)*binomial(j, i)*(j-2*i)^(n-m+j)/(n-m+j)!, i, 0, floor(j/2)), j, 1, k))*binomial(k+n-1, n-1), k, 1, n-m), m, 1, n-1)+(n-1)!;
(PARI) x='x+O('x^30); Vec(serlaplace(log(1/(1-asin(x))))) \\ G. C. Greubel, Jan 16 2018
CROSSREFS
Sequence in context: A309910 A042171 A133148 * A143599 A264409 A199202
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 02 2011
EXTENSIONS
Terms a(18) onward added by G. C. Greubel, Jan 16 2018
STATUS
approved