A352113
Expansion of e.g.f. (1 - log(1 - 3*x))^(1/3).
Original entry on oeis.org
1, 1, 1, 10, 64, 874, 11602, 214696, 4287376, 102791944, 2706467608, 80520419440, 2616373545040, 93309672227680, 3598524149027680, 149819807423180800, 6681701058862660480, 318224146460638476160, 16106859257541255648640, 863764371283534316220160
Offset: 0
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m = 19; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 3*x])^(1/3), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace((1-log(1-3*x))^(1/3)))
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a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, -3*j+1)*stirling(n, k, 1));
A352075
Expansion of e.g.f. sqrt(1 - log(1 - 2*x)).
Original entry on oeis.org
1, 1, 1, 5, 25, 209, 1961, 23589, 321105, 5100801, 90384369, 1792247973, 39011436201, 928869511569, 23953711043289, 666047439187077, 19847286284835105, 631267636613496705, 21339849019758468705, 764149215124570567365, 28891697037933017586105
Offset: 0
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m = 20; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 2*x])^(1/2), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(1-log(1-2*x))))
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a(n) = sum(k=0, n, (-2)^(n-k)*prod(j=0, k-1, -2*j+1)*stirling(n, k, 1));
A352123
Expansion of e.g.f. (2 - exp(-4*x))^(1/4).
Original entry on oeis.org
1, 1, -7, 73, -1135, 24241, -659767, 21796153, -846456415, 37772943841, -1904103268327, 106992035096233, -6630198107231695, 449171668238551441, -33024202381308836887, 2618743082761141212313, -222782402553043700662975, 20238957866498067052271041
Offset: 0
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m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-4*x])^(1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-4*x))^(1/4)))
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a(n) = sum(k=0, n, (-4)^(n-k)*prod(j=0, k-1, -4*j+1)*stirling(n, k, 2));
Showing 1-3 of 3 results.