A354286
Expansion of e.g.f. 1/(1 - x)^(2/(1 + 2 * log(1-x))).
Original entry on oeis.org
1, 2, 14, 144, 1936, 32000, 625952, 14117152, 360175584, 10246079616, 321313928448, 11006050602624, 408662128569984, 16344011453662464, 700254206319007488, 31990601456727585792, 1551985176120589820928, 79669906174753878177792
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^(2/(1+2*log(1-x)))))
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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, sum(k=0, j, 2^k*k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;
A354287
Expansion of e.g.f. 1/(1 - x)^(3/(1 + 3 * log(1-x))).
Original entry on oeis.org
1, 3, 30, 438, 8334, 194580, 5368662, 170591022, 6126386724, 245127214548, 10804866210648, 519910458588576, 27105081897342816, 1521393008601586536, 91445577404393807928, 5858664681621903625368, 398467273528657973600208, 28668189882264862351707504
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^(3/(1+3*log(1-x)))))
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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, sum(k=0, j, 3^k*k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;
A256548
Triangle read by rows, T(n,k) = |n,k|*h(k), where |n,k| are the Stirling cycle numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.
Original entry on oeis.org
1, 0, 1, 0, 1, 3, 0, 2, 9, 13, 0, 6, 33, 78, 73, 0, 24, 150, 455, 730, 501, 0, 120, 822, 2925, 6205, 7515, 4051, 0, 720, 5292, 21112, 53655, 87675, 85071, 37633, 0, 5040, 39204, 170716, 494137, 981960, 1304422, 1053724, 394353
Offset: 0
Triangle starts:
[1]
[0, 1]
[0, 1, 3]
[0, 2, 9, 13]
[0, 6, 33, 78, 73]
[0, 24, 150, 455, 730, 501]
[0, 120, 822, 2925, 6205, 7515, 4051]
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A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
A256548 = lambda n,k: A000262(k)*stirling_number1(n,k)
for n in range(7): [A256548(n,k) for k in (0..n)]
Showing 1-3 of 3 results.