A353891
Expansion of e.g.f. exp( (x * log(1-x))^2 / 4 ).
Original entry on oeis.org
1, 0, 0, 0, 6, 30, 165, 1050, 8932, 86184, 909360, 10393020, 129313206, 1743627600, 25314159780, 393346535400, 6512022804960, 114430467296880, 2127154061337480, 41703621476302800, 859966710771029040, 18606040434320713920, 421427283751799685360
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*log(1-x))^2/4)))
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a(n) = n!*sum(k=0, n\4, (2*k)!*abs(stirling(n-2*k, 2*k, 1))/(4^k*k!*(n-2*k)!));
A353892
Expansion of e.g.f. exp( -(x * log(1-x))^3 / 36 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 20, 210, 1960, 18900, 194880, 2166780, 26172080, 342599400, 4835694864, 73208215080, 1183011385920, 20318534134080, 369549843420384, 7094851788127680, 143377043010268800, 3042204544957939200, 67621161484919380800, 1571319471977711258880
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(x*log(1-x))^3/36)))
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a(n) = n!*sum(k=0, n\6, (3*k)!*abs(stirling(n-3*k, 3*k, 1))/(36^k*k!*(n-3*k)!));
A353896
Expansion of e.g.f. exp( (x * (exp(x) - 1))^4 / 576 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 13650, 115500, 841995, 5555550, 34139105, 198948750, 1144463320, 8171563400, 112204064700, 2364061354200, 49912312090845, 951208121086650, 16403948060775275, 260328078068154250, 3860274855288458376, 54182965918066177500
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^4/576)))
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a(n) = n!*sum(k=0, n\8, (4*k)!*stirling(n-4*k, 4*k, 2)/(576^k*k!*(n-4*k)!));
Showing 1-3 of 3 results.