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A351503
Expansion of e.g.f. 1/(1 + x^2 * log(1 - x)).
11
1, 0, 0, 6, 12, 40, 900, 6048, 43680, 717120, 8658720, 102231360, 1735525440, 28819964160, 473955850368, 9235543363200, 189202617676800, 3940225003653120, 89804740509434880, 2169337606086389760, 54085753764912844800, 1429100881569205125120
OFFSET
0,4
LINKS
FORMULA
a(0) = 1; a(n) = n! * Sum_{k=3..n} 1/(k-2) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/3)} k! * |Stirling1(n-2*k,k)|/(n-2*k)!.
MATHEMATICA
With[{nn=30}, CoefficientList[Series[1/(1+x^2 Log[1-x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 18 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=3, i, 1/(j-2)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\3, k!*abs(stirling(n-2*k, k, 1))/(n-2*k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 04 2022
STATUS
approved