A349965
a(n) = Sum_{k=0..n} (k * (n-k))^k.
Original entry on oeis.org
1, 1, 2, 7, 47, 513, 8020, 169227, 4637965, 159568981, 6684686230, 332681461871, 19316990453131, 1292074091000105, 98636639620170792, 8528989125071254867, 829516920337723299465, 90124512307642049807293, 10865612430780251465538154
Offset: 0
-
a[n_] := Sum[If[k == 0, 1, (k*(n - k))^k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)
-
a(n) = sum(k=0, n, (k*(n-k))^k);
A053729
Self-convolution of 1,4,27,256,3125,46656,... (cf. A000312).
Original entry on oeis.org
1, 8, 70, 728, 9027, 132136, 2254620, 44262200, 987183525, 24718587592, 687457908306, 21034757596184, 702270963692039, 25400848001674856, 989240042333246072, 41263578858484555512, 1835070614332428285513
Offset: 1
a(4) = 1^1 *4^4 +2^2 *3^3 +3^3 *2^2 +4^4 *1^1 = 1*256 +4*27 +27*4 +256*1 = 728.
-
nn=20;f[x_]=Sum[n^n x^n,{n,1,nn}];CoefficientList[Series[f[x]^2/x^2,{x,0,nn}],x] (* Geoffrey Critzer, Nov 05 2013 *)
Table[Sum[k^k*(n+1-k)^(n+1-k), {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 10 2018 *)
-
def A053729(n): return sum((k**k)*(n+1-k)**(n+1-k) for k in range(1,n+1)) # John Tyler Rascoe, Aug 23 2024
A349966
a(n) = Sum_{k=0..n} (k * (n-k))^n.
Original entry on oeis.org
1, 0, 1, 16, 418, 17600, 1086979, 92223488, 10292241540, 1462309109760, 257739952352133, 55188518041440256, 14111052911099343782, 4246668467339066589184, 1485904567816768099571207, 598145009954138900489830400
Offset: 0
-
a[0] = 1; a[n_] := Sum[(k*(n - k))^n, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Dec 07 2021 *)
-
a(n) = sum(k=0, n, (k*(n-k))^n);
A350008
a(n) = Sum_{k=0..n} k^(2*k).
Original entry on oeis.org
1, 2, 18, 747, 66283, 9831908, 2186614244, 680409687093, 282155386397749, 150376790683396870, 100150376790683396870, 81502899763630444510191, 79578350103154474577951727, 91812908543371771132977567736
Offset: 0
-
a[n_] := Sum[If[k == 0, 1, k^(2*k)], {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, Dec 08 2021 *)
-
a(n) = sum(k=0, n, k^(2*k));
A349874
Expansion of A(x)^3, where A(x) is g.f. of n^n (A000312).
Original entry on oeis.org
1, 3, 15, 106, 990, 11688, 168529, 2886039, 57372984, 1299676869, 33049616319, 931991169660, 28856822050546, 972979199567826, 35480222492288493, 1391109691131953417, 58351612093156552572, 2607190821521732751855, 123613763047459102476027
Offset: 0
-
nmax = 20; CoefficientList[Series[(1 + Sum[n^n * x^n, {n,1,nmax}])^3, {x,0,nmax}],x]
Showing 1-5 of 5 results.
Comments