A357967
Expansion of e.g.f. exp( x * (exp(x^3) - 1) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 20160, 0, 604800, 19958400, 79833600, 259459200, 25427001600, 326918592000, 1046139494400, 44460928512000, 1333827855360000, 10306043229081600, 125024130975744000, 6386367771463680000, 101695303941783552000, 861733891296165888000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3)-1))))
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a(n) = n!*sum(k=0, n\3, stirling(k, n-3*k, 2)/k!);
A375588
Expansion of e.g.f. 1 / (1 + x - x * exp(x^2)).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 720, 840, 40320, 378000, 2116800, 60207840, 598752000, 7792424640, 181863601920, 2288689603200, 45855781171200, 1016682053587200, 17113328962329600, 422970486434496000, 9765438564930048000, 213305542403822668800, 5916931500898517299200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/k!);
A357962
Expansion of e.g.f. exp( (exp(x^2) - 1)/x ).
Original entry on oeis.org
1, 1, 1, 4, 13, 51, 271, 1366, 8849, 58717, 432541, 3530176, 29787781, 279974839, 2715912291, 28415168146, 312503079841, 3600714035321, 43979791574809, 556150585730140, 7417561518005341, 102438949373356891, 1476634705941320311, 22102618328057267694
Offset: 0
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With[{nn=30},CoefficientList[Series[Exp[(Exp[x^2]-1)/x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 19 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((exp(x^2)-1)/x)))
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a(n) = n!*sum(k=0, n\2, stirling(n-k, n-2*k, 2)/(n-k)!);
A357968
Expansion of e.g.f. exp( x * (exp(x^4) - 1) ).
Original entry on oeis.org
1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 1814400, 0, 0, 1037836800, 43589145600, 217945728000, 0, 14820309504000, 1867358997504000, 30411275102208000, 101370917007360000, 425757851430912000, 140500090972200960000, 5385836820601036800000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^4)-1))))
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a(n) = n!*sum(k=0, n\4, stirling(k, n-4*k, 2)/k!);
A375591
Expansion of e.g.f. exp( x * (exp(x^2/2) - 1) ).
Original entry on oeis.org
1, 0, 0, 3, 0, 15, 90, 105, 2520, 8505, 66150, 634095, 3118500, 40675635, 285675390, 2896618725, 31556725200, 281774718225, 3691224687150, 37783760189175, 483465043561500, 6108282465360075, 76126660317858150, 1102221773079151725, 14598579860502838200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)-1))))
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a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/(2^k*k!));
A376351
E.g.f. satisfies A(x) = exp( x*A(x)*(exp(x^2*A(x)^2) - 1) ).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2520, 840, 181440, 6063120, 11642400, 1437337440, 44626982400, 254278664640, 24575197046400, 756010400745600, 9284429893939200, 784770965801222400, 25067890370095372800, 541810656586725926400, 42351473267452597248000, 1461224653966598493772800, 48020130717168717960652800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(x*(1-exp(x^2))))/x))
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a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*stirling(k, n-2*k, 2)/k!);
Showing 1-6 of 6 results.