A375660
Expansion of e.g.f. 1 / (1 - x * (exp(x) - 1))^2.
Original entry on oeis.org
1, 0, 4, 6, 80, 370, 4152, 34034, 413632, 4744674, 66354680, 954512482, 15454225536, 263909265074, 4898255210968, 96284064551250, 2022022344889472, 44858682139345090, 1052826609589372152, 25994393541984673154, 674563101823606851520, 18337775305498096349202
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*(exp(x)-1))^2))
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a(n) = n!*sum(k=0, n\2, (k+1)!*stirling(n-k, k, 2)/(n-k)!);
A375672
Expansion of e.g.f. 1 / (1 + x * log(1 - x))^3.
Original entry on oeis.org
1, 0, 6, 9, 168, 810, 11592, 103320, 1511808, 19350576, 315908640, 5127930720, 95386497984, 1843728194880, 38978317929600, 866801578406400, 20627303078937600, 516780346452733440, 13695223899883530240, 381043219813390540800, 11135125489382277811200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x))^3))
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a(n) = n!*sum(k=0, n\2, (k+2)!*abs(stirling(n-k, k, 1))/(n-k)!)/2;
A376382
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1))^3 ).
Original entry on oeis.org
1, 0, 6, 9, 588, 3435, 196038, 2504271, 143382648, 3105223155, 186676465890, 5932031027703, 382522369695876, 16267245179116971, 1137287705462533758, 60811389044325205695, 4631220227358066139248, 298002734705467572715491, 24748409310987998502582138
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1))^3)/x))
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a(n) = 3*n!*sum(k=0, n\2, (3*n+k+2)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+3)!;
A377680
Expansion of e.g.f. (1 + x * (exp(x) - 1))^3.
Original entry on oeis.org
1, 0, 6, 9, 84, 375, 1998, 11361, 60840, 299403, 1368930, 5906373, 24362748, 97019247, 375712470, 1422455625, 5286155088, 19340722707, 69831127242, 249265052301, 880927979940, 3086000399223, 10726216043070, 37020328044945, 126961071656184, 432900077950875
Offset: 0
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a(n) = n!*sum(k=0, n\2, k!*binomial(3, k)*stirling(n-k, k, 2)/(n-k)!);
Showing 1-4 of 4 results.