A358013
Expansion of e.g.f. 1/(1 - x^2 * (exp(x) - 1)).
Original entry on oeis.org
1, 0, 0, 6, 12, 20, 750, 5082, 23576, 453672, 5755770, 50894030, 841270452, 14694142476, 201442729670, 3552604015170, 73814245552560, 1369932831933392, 27860865121662066, 655240785723048726, 15052226249248287500, 357713461766745539700, 9416426612423343023742
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^2*(exp(x)-1))))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=3, i, 1/(j-2)!*v[i-j+1]/(i-j)!)); v;
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a(n) = n!*sum(k=0, n\3, k!*stirling(n-2*k, k, 2)/(n-2*k)!);
A375718
Expansion of e.g.f. 1 / sqrt(1 - x^3 * (exp(x) - 1)).
Original entry on oeis.org
1, 0, 0, 0, 12, 30, 60, 105, 15288, 136332, 794160, 3742695, 165156420, 2977295178, 34259966832, 307175369865, 8066201665200, 210501545175960, 3893163654156768, 56023707973290507, 1275541469736173820, 38629328708426716470, 991445561747177496960
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-x^3*(exp(x)-1))))
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a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+3)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
A370990
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*(exp(x) - 1)) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 120, 210, 201936, 1996344, 12701520, 64865790, 17053788840, 374788816116, 4944496679304, 50034166184730, 6390396135006240, 239770550508132720, 5363062998193560096, 89908444484550625014, 7402557588108228698040
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3*(exp(x)-1)))/x))
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a(n) = sum(k=0, n\4, (n+k)!*stirling(n-3*k, k, 2)/(n-3*k)!)/(n+1);
A375716
Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/6).
Original entry on oeis.org
1, 0, 0, 0, 4, 10, 20, 35, 3976, 35364, 205920, 970365, 37643980, 670990606, 7705037704, 69043474955, 1690055888080, 43135620048200, 793592298255936, 11401734214307769, 250361353418216340, 7380072768323315410, 187670442928777057480, 3868359812089009616071
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*(exp(x)-1))^(1/6)))
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a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
A375717
Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/3).
Original entry on oeis.org
1, 0, 0, 0, 8, 20, 40, 70, 9072, 80808, 470640, 2217930, 91956920, 1649007932, 18956858648, 169921752910, 4310715370080, 111302746115920, 2053356893604192, 29525879498171538, 660295352236840680, 19735183465373056100, 504257138580203577800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*(exp(x)-1))^(1/3)))
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a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+2)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
Showing 1-5 of 5 results.