A323660 -id:A323660 - cp's OEIS frontend

A323659 a(n) = Product_{k=0..n} (k^10 + (n-k)^10).

0, 1, 2097152, 3663302861300625, 7851806399838625464320000, 378407193115560358680820465087890625, 45364420795826382440918950445637925790023680000, 34139918620704541898946466431984113559562219610081631390625

Offset: 0

Vaclav Kotesovec, Jan 23 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..59

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323660, A323661, A323662.

Table[Product[k^10+(n-k)^10, {k, 0, n}], {n, 0, 10}]

a(n) ~ exp((Pi*(1/2 + 2*sqrt(5) - 2*sqrt(1 + 2/sqrt(5))) - 10)*n) * n^(10*n+10).

A323661 a(n) = Product_{k=0..n} (k^12 + (n-k)^12).

Original entry on oeis.org

0, 1, 33554432, 4740695283514005729, 651240623131512957219821846528, 4811704081770214536604871809482574462890625, 84537031377296019762303015000377965680906643309559021568, 16210797840416801857079558076889164370156937375891800497483902744790721

Offset: 0

Vaclav Kotesovec, Jan 23 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..51

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323660, A323662.

Table[Product[k^12+(n-k)^12, {k, 0, n}], {n, 0, 10}]

a(n) ~ exp((Pi*(-5/2 + 2*sqrt(6) + sqrt(2*(5-2*sqrt(6))/3)) - 12)*n) * n^(12*n+12).

A323662 a(n) = Product_{k=0..n} (k^13 + (n-k)^13).

Original entry on oeis.org

0, 1, 134217728, 170623376651175378921, 187556828900191806607614608932864, 17233921359224498311699145473539829254150390625, 3651108402083969086976039852657366429953837378356052425179136

Offset: 0

Vaclav Kotesovec, Jan 23 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..48

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323660, A323661.

Table[Product[k^13+(n-k)^13, {k, 0, n}], {n, 0, 10}]

a(n) ~ exp((2*Pi*sqrt((2699 - 1920*cos(2*Pi/13) + 4184*cos(3*Pi/13) - 4512*sin(Pi/26) + 4752*sin(3*Pi/26) - 2944*sin(5*Pi/26))/13) / 13 - 12)*n) * n^(13*n+13).

cp's OEIS Frontend

A323659 a(n) = Product_{k=0..n} (k^10 + (n-k)^10).

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A323661 a(n) = Product_{k=0..n} (k^12 + (n-k)^12).

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A323662 a(n) = Product_{k=0..n} (k^13 + (n-k)^13).

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