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)!));
A353895
Expansion of e.g.f. exp( (x * (exp(x) - 1))^3 / 36 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 850300, 9875580, 170133964, 2688015330, 36706233200, 444802722000, 4939264076016, 52543545234534, 583037908936500, 7645631225897700, 124931080233222340, 2327407301807577066, 44282377224446369800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^3/36)))
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a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(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.