A357265
Expansion of e.g.f. -LambertW(x * log(1-x)).
Original entry on oeis.org
0, 0, 2, 3, 32, 150, 1884, 16380, 249808, 3255336, 59596560, 1037413080, 22432698144, 486784686960, 12233449250736, 316660035739320, 9111729094222080, 273147758526888000, 8880267446524694016, 301952732236006556160, 10963551960785051470080
Offset: 0
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my(N=20, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(-lambertw(x*log(1-x)))))
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a(n) = n!*sum(k=1, n\2, k^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A355179
Expansion of e.g.f. -LambertW(x^2 * (1 - exp(x)))/2.
Original entry on oeis.org
0, 0, 0, 3, 6, 10, 375, 2541, 11788, 317556, 4238685, 37921015, 909616026, 18283276518, 261259582675, 6360432558585, 164704011195480, 3332419310132776, 88606184592031353, 2713050497589230763, 71412977041725823750, 2144089948615678382970
Offset: 0
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With[{nn=30},CoefficientList[Series[(-LambertW[x^2 (1-Exp[x])])/2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 07 2025 *)
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my(N=20, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2*(1-exp(x)))/2)))
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a(n) = n!*sum(k=1, n\3, k^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!)/2;
A355180
Expansion of e.g.f. -LambertW(x^3 * (1 - exp(x)))/6.
Original entry on oeis.org
0, 0, 0, 0, 4, 10, 20, 35, 6776, 60564, 352920, 1663365, 126625180, 2361079006, 27334747804, 245495250455, 11174333090480, 328952158255400, 6245314009946736, 90576650639967369, 3209305759254634740, 122557203047084965810, 3365068665450300234580
Offset: 0
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my(N=20, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3*(1-exp(x)))/6)))
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a(n) = n!*sum(k=1, n\4, k^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!)/6;
A355181
Expansion of e.g.f. -LambertW(x^2/2 * (1 - exp(x))).
Original entry on oeis.org
0, 0, 0, 3, 6, 10, 195, 1281, 5908, 90756, 1098765, 9605035, 147947646, 2496239538, 33836915203, 588360763095, 12104789358600, 223722576473896, 4578806487368313, 108875473376842467, 2519418390663035170, 60831875074927797750, 1640260621340460494991
Offset: 0
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my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2/2*(1-exp(x))))))
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a(n) = n!*sum(k=1, n\3, k^(k-1)*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));
A355308
Expansion of e.g.f. -LambertW(x^3/6 * (1 - exp(x))).
Original entry on oeis.org
0, 0, 0, 0, 4, 10, 20, 35, 1176, 10164, 58920, 277365, 4472380, 69189406, 772011604, 6861855455, 95279504880, 1819310613800, 30768119885136, 430200439251369, 6770486332450740, 139958614722287410, 3033142442978720380, 58782387380290683571, 1138026666874389737544
Offset: 0
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my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3/6*(1-exp(x))))))
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a(n) = n!*sum(k=1, n\4, k^(k-1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
Showing 1-5 of 5 results.