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
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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)))
A384325
Expansion of Product_{k>=1} 1/(1 - k*x)^((3/4)^k).
Original entry on oeis.org
1, 12, 114, 1084, 11319, 136920, 1981228, 34705656, 731268315, 18203860748, 524073230394, 17111173850652, 623571696107069, 25046605210733184, 1097919954149781264, 52109508350206511840, 2660615337817983390318, 145353541761618312219336
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, sum(j=0, k, 3^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
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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)))
Showing 1-3 of 3 results.