A355463
Expansion of Sum_{k>=0} (x/(1 - k^k * x))^k.
Original entry on oeis.org
1, 1, 2, 10, 131, 5656, 869097, 490286392, 1264458639313, 12443651667592768, 681538604797281047489, 153070077563816488157872384, 205935348854901274982393017521537, 1352544986573612111579941739713633174912
Offset: 0
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Flatten[{1, Table[Sum[Binomial[n-1,k-1] * k^(k*(n-k)), {k,1,n}], {n,1,20}]}] (* Vaclav Kotesovec, Feb 16 2023 *)
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^k*x))^k))
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a(n) = if(n==0, 1, sum(k=1, n, k^(k*(n-k))*binomial(n-1, k-1)));
A355496
Expansion of Sum_{k>=0} (k^3 * x/(1 - x))^k.
Original entry on oeis.org
1, 1, 65, 19812, 16836458, 30584805344, 101712712528352, 559155681922806328, 4726278437746021089208, 58187531579876705928027712, 1000523517685151396828602120640, 23235157037192774575979788565151104, 709057406693306876515431403267191583808
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x/(1-x))^k))
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a(n) = if(n==0, 1, sum(k=1, n, k^(3*k)*binomial(n-1, k-1)));
A355471
Expansion of Sum_{k>=0} (x/(1 - k^2 * x))^k.
Original entry on oeis.org
1, 1, 2, 10, 77, 808, 11257, 196072, 4136897, 103755904, 3034193921, 101901347944, 3885951145969, 166605168800704, 7961498177012993, 420976047757358776, 24475992585921169553, 1556007778666449968128, 107625967130820901112833
Offset: 0
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Flatten[{1, Table[Sum[Binomial[n-1,k-1] * k^(2*(n-k)), {k,1,n}], {n,1,20}]}] (* Vaclav Kotesovec, Feb 16 2023 *)
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^2*x))^k))
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a(n) = if(n==0, 1, sum(k=1, n, k^(2*(n-k))*binomial(n-1, k-1)));
Showing 1-3 of 3 results.