A354310
Expansion of e.g.f. 1/(1 - 3*x)^(x/3).
Original entry on oeis.org
1, 0, 2, 9, 84, 990, 14754, 264600, 5549424, 133217784, 3601384200, 108249692760, 3580724721672, 129250420556400, 5055196156459344, 212951257371183240, 9612027759287831040, 462798880374787387200, 23675607840207619145664, 1282413928716141429168000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^(x/3)))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
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a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*abs(stirling(n-k, k, 1))/(n-k)!);
A354311
Expansion of e.g.f. exp( x/2 * (exp(2 * x) - 1) ).
Original entry on oeis.org
1, 0, 2, 6, 28, 160, 1056, 7784, 63568, 569664, 5542240, 58038112, 650045760, 7746901760, 97790608384, 1302349549440, 18235836899584, 267663541270528, 4107395264113152, 65739857693144576, 1095095457262013440, 18949711553467957248, 340036076121127395328
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/2*(exp(2*x)-1))))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*2^(j-2)*binomial(i-1, j-1)*v[i-j+1])); v;
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a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*stirling(n-k, k, 2)/(n-k)!);
A354315
Expansion of e.g.f. 1/(1 + x/2 * log(1 - 2 * x)).
Original entry on oeis.org
1, 0, 2, 6, 56, 480, 5664, 75600, 1182208, 20829312, 410768640, 8943010560, 213187497984, 5520777799680, 154333888579584, 4631752470159360, 148523272512307200, 5067610703150284800, 183308248516478828544, 7006773595450681589760, 282194468488468121518080
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/2*log(1-2*x))))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 2^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
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a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
A354319
Expansion of e.g.f. 1/(1 - 2*x)^(x/4).
Original entry on oeis.org
1, 0, 1, 3, 19, 150, 1497, 17955, 251681, 4036284, 72874125, 1462571055, 32297755803, 778188449610, 20313917363733, 571081958323695, 17201321168216385, 552635193533958360, 18863471310967732473, 681711909339186154395, 26003437607893415476995
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x)^(x/4)))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*2^(j-3)/(j-1)*v[i-j+1]/(i-j)!)); v;
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a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*abs(stirling(n-k, k, 1))/(n-k)!);
Showing 1-4 of 4 results.