A375701
Expansion of e.g.f. 1 / sqrt(1 + x^3 * log(1 - x)).
Original entry on oeis.org
1, 0, 0, 0, 12, 30, 120, 630, 19152, 166320, 1506600, 14968800, 313014240, 4864860000, 72829607760, 1116874558800, 23605893400320, 495461472105600, 10289649464640000, 215706738207542400, 5222625647551920000, 133507746422859513600, 3481696859911699968000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+x^3*log(1-x))))
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a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+3)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));
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)))
-
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 1-3 of 3 results.