A355464
Expansion of Sum_{k>=0} x^k/(1 - k^k * x)^(k+1).
Original entry on oeis.org
1, 2, 4, 17, 210, 9217, 1399298, 811229225, 2071392232962, 20710319937493889, 1137259214532706572162, 255141201504146525745627265, 348787971214016591166179037803522, 2262996819897931095524655885144485185409
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^k*x)^(k+1)))
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*x^k/k!)))
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a(n) = sum(k=0, n, k^(k*(n-k))*binomial(n, k));
A355470
Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1).
Original entry on oeis.org
1, 1, 66, 21222, 18927560, 36030104000, 125486684755152, 722272396672485568, 6391048590559497227904, 82362961035803105954736768, 1482370265813455598541301007360, 36031982428595760278113744699088384, 1150873035676373345725887922070318410752
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-k^3*x)^(k+1)))
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*(k^3*x)^k/k!)))
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a(n) = sum(k=0, n, k^(3*n)*binomial(n, k));
A355493
Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - x)^(k+1).
Original entry on oeis.org
1, 2, 67, 19879, 16856337, 30601661681, 101743314190033, 559257425236996361, 4726837695171258085569, 58192258417571877186113281, 1000581709943568968705788233921, 23236157618902718144948494353385025, 709080642850925779233576351761544968833
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-x)^(k+1)))
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k^3*x)^k/k!)))
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a(n) = sum(k=0, n, k^(3*k)*binomial(n, k));
Showing 1-3 of 3 results.