A371230
E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 128, 750, 29964, 377160, 15795072, 329631120, 15001287120, 449174341440, 22551082739712, 885381886509120, 49302509206648320, 2391802812599316480, 147728974730632012800, 8502972330919072688640, 580806950108814502345728
Offset: 0
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terms=19; A[]=1; Do[A[x]= 1 - x*A[x]^3*Log[1 - x*A[x]^2] + O[x]^terms//Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]*Range[0,terms-1]! (* Stefano Spezia, Sep 03 2025 *)
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a(n) = n!*sum(k=0, n\2, (2*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(2*n+1)!;
A376386
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ).
Original entry on oeis.org
1, 0, 6, 9, 600, 3510, 204372, 2617020, 152727936, 3319236144, 203151929040, 6485780434320, 425284393933440, 18190896271479360, 1291781802823916544, 69545182272420909600, 5374429456543444177920, 348502600060029871948800, 29344904433432469953368064
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x))^3)/x))
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a(n) = 3*n!*sum(k=0, n\2, (3*n+k+2)!*abs(stirling(n-k, k, 1))/(n-k)!)/(3*n+3)!;
A371273
E.g.f. satisfies A(x) = 1 + x*A(x)^4 * (exp(x*A(x)^3) - 1).
Original entry on oeis.org
1, 0, 2, 3, 172, 1025, 54606, 710017, 38964024, 855167553, 49992166090, 1603665906161, 101454726848388, 4342187407054081, 299554876119595110, 16084216120063348545, 1213404824364026124016, 78279943651487041769345, 6456915976418046368634402
Offset: 0
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a(n) = n!*sum(k=0, n\2, (3*n+k)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+1)!;
A376387
Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + x*log(1-x))^3 ) )^(2/3).
Original entry on oeis.org
1, 0, 4, 6, 376, 2220, 125028, 1614480, 92285856, 2018520000, 121850616240, 3907998135360, 253836993367296, 10891474747433280, 768302761361304960, 41447634607068318720, 3187906294983450762240, 206982374312337802536960, 17368877655215923728595968
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+x*log(1-x))^3)/x)^(2/3)))
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a(n) = 2*n!*sum(k=0, n\2, (3*n+k+1)!*abs(stirling(n-k, k, 1))/(n-k)!)/(3*n+2)!;
Showing 1-4 of 4 results.