A354134
Expansion of e.g.f. 1/(1 - log(1 + x)^3/6).
Original entry on oeis.org
1, 0, 0, 1, -6, 35, -205, 1204, -6692, 29084, 17160, -3069924, 61356724, -959574408, 13499619224, -174983776176, 2029529618080, -18417948918640, 36189097244720, 4235753092128480, -157628320980720480, 4166967770825777280, -95152715945973322560
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x)^3/6)))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, binomial(i, j)*stirling(j, 3, 1)*v[i-j+1])); v;
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a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 1)/6^k);
A354137
Expansion of e.g.f. exp(log(1 + x)^5/120).
Original entry on oeis.org
1, 0, 0, 0, 0, 1, -15, 175, -1960, 22449, -269199, 3410000, -45753180, 650179816, -9771920158, 155020385156, -2589888417480, 45461879164584, -836540418765834, 16099972965770778, -323385447259166454, 6764948641797695496, -147088325599708573080
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)^5/120)))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, binomial(i-1, j-1)*stirling(j, 5, 1)*v[i-j+1])); v;
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a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 1)/(120^k*k!));
A354230
Expansion of e.g.f. 1/(1 - log(1 + x)^5).
Original entry on oeis.org
1, 0, 0, 0, 0, 120, -1800, 21000, -235200, 2693880, -28690200, 210447600, 1465952400, -123513355680, 4155643171680, -114924516470400, 2886135295680000, -66750668391381120, 1375830884058456960, -22036006671394705920, 70186623981895296000, 16180846322732941893120
Offset: 0
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With[{nn=30},CoefficientList[Series[1/(1-Log[1+x]^5),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 20 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x)^5)))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=120*sum(j=1, i, binomial(i, j)*stirling(j, 5, 1)*v[i-j+1])); v;
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a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 1));
Showing 1-3 of 3 results.