A360774
Expansion of Sum_{k>=0} (x * (k + x))^k.
Original entry on oeis.org
1, 1, 5, 31, 284, 3390, 49878, 871465, 17620450, 404554997, 10394845097, 295485704544, 9205957047661, 311922101632409, 11419004058232897, 449146827324857447, 18889836751306735360, 845892838094616177138, 40182354573647684880446
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x))^k))
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a(n) = sum(k=0, n\2, (n-k)^(n-2*k)*binomial(n-k, k));
A360776
Expansion of Sum_{k>=0} (x * (k + x^3))^k.
Original entry on oeis.org
1, 1, 4, 27, 257, 3129, 46683, 823799, 16780342, 387467154, 10000823639, 285328449077, 8916487888186, 302885106945216, 11112292144568909, 437902806653498835, 18447046953316227905, 827251374022851280231, 39346845973273509115167
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x^3))^k))
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a(n) = sum(k=0, n\4, (n-3*k)^(n-4*k)*binomial(n-3*k, k));
A360770
Expansion of Sum_{k>0} (x * (k + x^k))^k.
Original entry on oeis.org
1, 5, 27, 260, 3125, 46684, 823543, 16777472, 387420498, 10000003125, 285311670611, 8916100495009, 302875106592253, 11112006826381559, 437893890380860625, 18446744073726328848, 827240261886336764177, 39346408075296925015353
Offset: 1
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a[n_] := DivisorSum[n, #^(# - n/# + 1) * 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, (x*(k+x^k))^k))
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a(n) = sumdiv(n, d, d^(d-n/d+1)*binomial(d, n/d-1));
Showing 1-3 of 3 results.