A360726
Expansion of Sum_{k>0} (k * x * (1 + x^k))^k.
Original entry on oeis.org
1, 5, 27, 264, 3125, 46741, 823543, 16778240, 387420570, 10000015625, 285311670611, 8916100729755, 302875106592253, 11112006831322817, 437893890380890625, 18446744073843770368, 827240261886336764177, 39346408075300025059665
Offset: 1
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a[n_] := DivisorSum[n, #^# * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+x^k))^k))
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a(n) = sumdiv(n, d, d^d*binomial(d, n/d-1));
A360733
Expansion of Sum_{k>0} (x * (1 + (k * x)^k))^k.
Original entry on oeis.org
1, 2, 1, 9, 1, 98, 1, 1025, 2188, 15626, 1, 692836, 1, 5764802, 97656251, 201326593, 1, 36138519442, 1, 409470748547, 14242684529830, 3138428376722, 1, 10019491686645761, 476837158203126, 3937376385699290, 5403406870691968357, 19704673338472752470, 1
Offset: 1
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a[n_] := DivisorSum[n, #^(n-#) * Binomial[#, n/# - 1] &]; Array[a, 30] (* Amiram Eldar, Aug 09 2023 *)
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my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (x*(1+(k*x)^k))^k))
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a(n) = sumdiv(n, d, d^(n-d)*binomial(d, n/d-1));
A360754
Expansion of Sum_{k>0} (k * x * (1 + (2 * x)^k))^k.
Original entry on oeis.org
1, 6, 27, 288, 3125, 47368, 823543, 16793600, 387425673, 10000500000, 285311670611, 8916118771200, 302875106592253, 11112007563452544, 437893890412859375, 18446744108073484288, 827240261886336764177, 39346408077084637733376
Offset: 1
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a[n_] := DivisorSum[n, 2^(n-#) * #^# * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+(2*x)^k))^k))
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a(n) = sumdiv(n, d, 2^(n-d)*d^d*binomial(d, n/d-1));
Showing 1-3 of 3 results.