A375664
Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^2.
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 2160, 1680, 120960, 1481760, 6350400, 240166080, 2754259200, 31152401280, 894303970560, 11769588230400, 228232766361600, 5845147711603200, 98290727395660800, 2502848611354291200, 63417766359467520000, 1376904298716724377600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(k, n-2*k, 2)/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;
A375811
Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x)^3.
Original entry on oeis.org
1, 3, 12, 69, 504, 4380, 44280, 509670, 6572160, 93813552, 1467910080, 24976440720, 459045195840, 9061616266560, 191187467190720, 4293103436622000, 102216550583347200, 2572022267758944000, 68195046359419499520, 1900236334204732043520
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^3))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*stirling(n-k, n-2*k, 2)/(n-k)!)/2;
A376444
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^3 ).
Original entry on oeis.org
1, 0, 0, 18, 0, 180, 23760, 2520, 1693440, 180033840, 107956800, 42093263520, 4131388800000, 7363478041920, 2262271571239680, 213613512570057600, 843365230060953600, 226557537882970694400, 20988751571439158707200, 154613821575430253836800, 38125864157166326661120000, 3508865828606684108929766400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^3)/x))
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a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/(3*n+3)!;
Showing 1-4 of 4 results.