A375663
Expansion of e.g.f. 1 / (1 - x^2 * (exp(x) - 1))^3.
Original entry on oeis.org
1, 0, 0, 18, 36, 60, 4410, 30366, 141288, 4173336, 56307150, 504947850, 10795641516, 209176625268, 2958760573314, 60807476490390, 1419440085948240, 27655117897680816, 621153635750802198, 16250306025184563330, 396542042830732066260, 10152940698142734694860
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^2*(exp(x)-1))^3))
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a(n) = n!*sum(k=0, n\3, (k+2)!*stirling(n-2*k, k, 2)/(n-2*k)!)/2;
A375639
Expansion of e.g.f. 1 / (1 + x^2 * log(1 - x))^2.
Original entry on oeis.org
1, 0, 0, 12, 24, 80, 2520, 17136, 124320, 2462400, 30965760, 372113280, 7014807360, 122840789760, 2078973921024, 43236813312000, 932206147891200, 20090534745415680, 480054835899371520, 12126262777282805760, 313198020852233932800
Offset: 0
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With[{nn=20},CoefficientList[Series[1/(1+x^2 Log[1-x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 29 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2*log(1-x))^2))
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a(n) = n!*sum(k=0, n\3, (k+1)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!);
A376438
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*(exp(x) - 1))^2 ).
Original entry on oeis.org
1, 0, 0, 12, 24, 40, 10860, 85764, 446992, 57788784, 1008736020, 10835748220, 965748698904, 28637803537512, 519426455756572, 37968161216666100, 1626852405783259680, 44177643556314690784, 2957776991432290423332, 163869985958022692795628, 6132727345895339422510120, 405409522521171206216078040
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*(exp(x)-1))^2)/x))
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a(n) = 2*n!*sum(k=0, n\3, (2*n+k+1)!*stirling(n-2*k, k, 2)/(n-2*k)!)/(2*n+2)!;
Showing 1-3 of 3 results.