A353880
Expansion of e.g.f. 1/(1 - (x * log(1-x))^2 / 4).
Original entry on oeis.org
1, 0, 0, 0, 6, 30, 165, 1050, 10192, 108864, 1230660, 14758920, 195861996, 2852815680, 44880446520, 753211040400, 13458760362720, 255688784416800, 5149255813778160, 109489194918180000, 2450182706364430080, 57567025900160259840, 1417073899136197468320
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(n-2*k)!));
A353884
Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^3 / 36).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 1035100, 17082780, 329893564, 5336661330, 73265956400, 889068944400, 9968073461616, 112902000191334, 1531070090032500, 27610559023112100, 586336131631313140, 12550716321612658266, 254052845940651258600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(n-3*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)!));
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 1-4 of 4 results.