A384324
Expansion of Product_{k>=1} 1/(1 - k*x)^((2/3)^k).
Original entry on oeis.org
1, 6, 33, 200, 1428, 12408, 132604, 1730160, 27043866, 495026316, 10388326986, 245555445888, 6446710871724, 185904786328920, 5836500883321164, 198054400887909264, 7220679972923312487, 281402128806812402490, 11671796413017231008663
Offset: 0
-
terms = 20; A[] = 1; Do[A[x] = -2*A[x] + 3*A[x/(1-x)]^(2/3) / (1-x)^2 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* Vaclav Kotesovec, May 27 2025 *)
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my(N=20, x='x+O('x^N)); Vec(exp(3*sum(k=1, N, sum(j=0, k, 2^j*j!*stirling(k, j, 2))*x^k/k)))
A384326
Expansion of Product_{k>=1} 1/(1 - k*x)^((4/5)^k).
Original entry on oeis.org
1, 20, 290, 3940, 55695, 872904, 15862460, 343510120, 8931896095, 276115329860, 9954870557826, 410042908659060, 18954497571869745, 969420292296268320, 54253252462944958560, 3293672518482920204544, 215400856153695252763320, 15088195059520554250863840
Offset: 0
-
terms = 20; A[] = 1; Do[A[x] = -4*A[x] + 5*A[x/(1-x)]^(4/5) / (1-x)^4 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* Vaclav Kotesovec, May 27 2025 *)
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my(N=20, x='x+O('x^N)); Vec(exp(5*sum(k=1, N, sum(j=0, k, 4^j*j!*stirling(k, j, 2))*x^k/k)))
A384305
Expansion of Product_{k>=1} 1/(1 - k*x)^((5/6)^k).
Original entry on oeis.org
1, 30, 615, 11260, 205695, 4013406, 88035585, 2255192280, 68859250020, 2506898720040, 107238427737876, 5281094776037040, 293625956135692020, 18139856902224931080, 1229886945212115522060, 90641666662687182976896, 7206758883035555464430370, 614391718014749017022916060
Offset: 0
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terms = 20; A[] = 1; Do[A[x] = -5*A[x] + 6*A[x/(1-x)]^(5/6) / (1-x)^5 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* Vaclav Kotesovec, May 31 2025 *)
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my(N=20, x='x+O('x^N)); Vec(exp(6*sum(k=1, N, sum(j=0, k, 5^j*j!*stirling(k, j, 2))*x^k/k)))
A384333
Expansion of Product_{k>=1} (1 + k*x)^((3/4)^k).
Original entry on oeis.org
1, 12, 30, 76, -819, 15120, -320568, 7719984, -208986462, 6300545128, -209806494828, 7660698340008, -304718887446110, 13127557400200944, -609336227455254936, 30330991088734345200, -1612305658103085757467, 91179423240593288760396, -5467060640706775435713298
Offset: 0
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terms = 20; A[] = 1; Do[A[x] = -3*A[x] + 4*A[x/(1+x)]^(3/4) * (1+x)^3 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* Vaclav Kotesovec, May 27 2025 *)
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my(N=20, x='x+O('x^N)); Vec(exp(4*sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 3^j*j!*stirling(k, j, 2))*x^k/k)))
Showing 1-4 of 4 results.