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!);
A375562
Expansion of e.g.f. 1 / (1 + x * log(1 - x^3)).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 1209600, 39916800, 479001600, 1556755200, 79913433600, 1961511552000, 25107347865600, 296406190080000, 11204153985024000, 263564384219136000, 4284610758844416000, 95795516571955200000, 3345240261242880000000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/k!);
A375680
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^2.
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 2160, 3360, 120960, 1632960, 9979200, 255467520, 3592512000, 45664819200, 1070840010240, 18027225216000, 340344048844800, 8174882722406400, 169308486085939200, 4019018956285132800, 104511967278630912000, 2606273308503760896000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2))^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!);
A375681
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^3.
Original entry on oeis.org
1, 0, 0, 18, 0, 180, 4320, 5040, 241920, 3900960, 19958400, 622702080, 9580032000, 112086374400, 3013462932480, 52540488000000, 977094287769600, 25683596370432000, 540291743902310400, 13061642656398336000, 360218657273739264000, 9111103133582241792000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2))^3))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(k, n-2*k, 1))/k!)/2;
A376344
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2)) ).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2880, 1680, 201600, 8074080, 19958400, 1824197760, 69854400000, 436929292800, 36099561738240, 1392369634656000, 17026966410854400, 1344523178718720000, 54023115000830976000, 1095484919871908966400, 84994409643640713216000, 3650011125774294048768000, 109122812080533877712486400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2)))/x))
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a(n) = sum(k=0, n\2, (2*n-2*k)!*abs(stirling(k, n-2*k, 1))/k!)/(n+1);
Showing 1-5 of 5 results.