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)!));
A353893
Expansion of e.g.f. exp( (x * log(1-x))^4 / 576 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 17850, 242550, 3350655, 48108060, 724403680, 11478967500, 191601229820, 3367499575440, 62253354650760, 1208755315895400, 24611454394536780, 524613603866302440, 11687734234226039220, 271715852337632107020
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*log(1-x))^4/576)))
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a(n) = n!*sum(k=0, n\8, (4*k)!*abs(stirling(n-4*k, 4*k, 1))/(576^k*k!*(n-4*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)!));
Showing 1-3 of 3 results.