A353881
Expansion of e.g.f. 1/(1 + (x * log(1-x))^3 / 36).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 20, 210, 1960, 18900, 194880, 2166780, 26356880, 349806600, 5029088064, 77748751080, 1284349422720, 22551300670080, 419191223208384, 8222848137607680, 169760091173740800, 3679746265902067200, 83564915096633308800, 1984162781781147770880
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(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*(n-3*k)!));
A353883
Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^2 / 4).
Original entry on oeis.org
1, 0, 0, 0, 6, 30, 105, 315, 3388, 47628, 497115, 4172025, 37829946, 491971194, 7699457857, 114432747975, 1602464966040, 23767387469688, 408590795439351, 7756561553900085, 149537297087139910, 2889288053301888630, 58297667473293537597
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(n-2*k)!));
A353885
Expansion of e.g.f. 1/(1 - (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, 1175994820, 10315705400, 192609389700, 4563951046200, 98992258506345, 1898260633492650, 32787422848455275, 520556451785466250, 7722233521138092726, 108688302800107222500
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(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 1-4 of 4 results.