A354328
Expansion of e.g.f. 1/(1 + x/8 * log(1 - 4 * x)).
Original entry on oeis.org
1, 0, 1, 6, 70, 1080, 21162, 501060, 13904152, 442241856, 15855648120, 632501646480, 27781645311216, 1332152096109120, 69237728070951888, 3876953348374273440, 232666700169003442560, 14897335773169370787840, 1013656610215024983681408
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/8*log(1-4*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, 4^(j-2)/(j-1)*v[i-j+1]/(i-j)!)/2); v;
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a(n) = n!*sum(k=0, n\2, 4^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(2^k*(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 1-3 of 3 results.