A363661
a(n) = Sum_{d|n} (n/d)^d * binomial(d+n,n).
Original entry on oeis.org
2, 12, 32, 150, 282, 1890, 3488, 21582, 54650, 282612, 705564, 4072224, 10400782, 55006530, 158987232, 790611350, 2333606526, 11573213196, 35345264180, 168673694070, 540848064614, 2500462200182, 8233430728152, 37445946291600, 126411051769652
Offset: 1
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f:= proc(n) local d;
add((n/d)^d * binomial(n+d,n), d = numtheory:-divisors(n))
end proc:
map(f, [$1..30]); # Robert Israel, Nov 23 2023
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a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n, n] &]; Array[a, 30] (* Amiram Eldar, Jul 05 2023 *)
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a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n, n));
A363664
a(n) = Sum_{d|n} (n/d)^(n-n/d) * binomial(d+n-1,n).
Original entry on oeis.org
1, 4, 11, 56, 127, 1100, 1717, 19300, 64406, 383010, 352717, 23214660, 5200301, 191172406, 3465549077, 20859527460, 1166803111, 1010698826825, 17672631901, 102589250081802, 286539905316908, 75260204476154, 4116715363801, 548610025890719156
Offset: 1
-
a[n_] := DivisorSum[n, (n/#)^(n-n/#) * Binomial[# + n - 1, n] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)
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a(n) = sumdiv(n, d, (n/d)^(n-n/d)*binomial(d+n-1, n));
A363666
a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-2,n-1).
Original entry on oeis.org
1, 3, 7, 29, 71, 355, 925, 4425, 13276, 60111, 184757, 856357, 2704157, 12137147, 40367461, 176999505, 601080391, 2616894901, 9075135301, 38884056181, 138014377810, 583674491643, 2104098963721, 8823912454489, 32247616479976, 133998376789707
Offset: 1
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a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n - 2, n - 1] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)
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a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n-2, n-1));
Showing 1-3 of 3 results.
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