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)!));
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)!));
A353894
Expansion of e.g.f. exp( (x * (exp(x) - 1))^2 / 4 ).
Original entry on oeis.org
1, 0, 0, 0, 6, 30, 105, 315, 2128, 24948, 251415, 2093025, 16437036, 148728294, 1693067467, 21459867975, 270217289280, 3338860150488, 42428729660751, 581966068060485, 8654787480759700, 135253842794286930, 2163416823356628147, 35313421249845594075
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^2/4)))
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a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*k!*(n-2*k)!));
Showing 1-3 of 3 results.