A023813 -id:A023813 - cp's OEIS frontend

A120929 Partial sums of n^(n^2), A002489.

1, 2, 18, 19701, 4294986997, 298023228171940122, 10314424798788558774343889178, 256923577521069192513410265783009965210785, 6277101735386681020759366944276858929512621227473999723681

Offset: 0

Jonathan Vos Post, Aug 18 2006

After 2, can this ever be prime? This is to A001923 Sum k^k, k=1..n, as k^k^k is to k^k.

			a(0) = 1 because A002489(0) is given formally as 0^0^0 = 1.
a(1) = 2 because 1 + (1^1)^1 = 1 + 1 = 2.
a(2) = 18 because 2 + (2^2)^2 = 2 + 16 = 18.
a(3) = 19701 because 18 + (3^3)^3 = 18 + 19683 = 19701.
a(4) = 4294986997 = 19701 + (4^4)^4 = 19701 + 4294967296.

Seiichi Manyama, Table of n, a(n) for n = 0..26

Cf. A001923, A002489, A002488, A001329, A002488, A023813, A076113, A090588.

Accumulate[Join[{1},Table[n^(n^2),{n,9}]]] (* Harvey P. Dale, Apr 10 2014 *)

a(n) = Sum_{i=0..n} i^(i^2). a(n) = Sum_{i=0..n} (i^i)^i. In this sequence, we formally define 0^0 = 1.

More terms from Harvey P. Dale, Apr 10 2014

A366355 a(n) = (-1)^n * QPochhammer(n, n, n).

Original entry on oeis.org

1, 0, 3, 416, 722925, 23205371904, 17674407688984375, 384914699001548351078400, 278893192683059452825059069034425, 7650586837724400321220283274999910891520000, 8900101000088880011112998877890031110997889100010099891

Offset: 0

Vaclav Kotesovec, Oct 08 2023

nonn

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Cf. A023813.

Table[(-1)^n * QPochhammer[n, n, n], {n, 0, 12}]
Join[{1}, Table[Product[Sum[n^j, {j, 1, k}], {k, 1, n}] * (1 - 1/n)^n, {n, 1, 12}]]

For n>0, a(n) = (1 - 1/n)^n * Product_{k=1..n} Sum_{j=1..k} n^j.

a(n) ~ n^(n*(n+1)/2).

A366361 a(n) is the permanent of the n X n matrix M(n) defined by M[i, j, n] = binomial(n*i, j).

Original entry on oeis.org

1, 1, 16, 8343, 191379456, 243158252171875, 20790955151695025307648, 141077987559931565709345896142747, 87560777683393072753972141033294994323013632, 5630148253059996156951223684618938659855264355379747814715, 41903151415731168301895742189359145224747037005872123307731920000000000000

Offset: 0

Stefano Spezia, Oct 08 2023

nonn

			a(3) = 8343:
  [3,  3,  1]
  [6, 15, 20]
  [9, 36, 84]

Cf. A023813 (determinant).

a[n_]:=Permanent[Table[Binomial[n i,j],{i,n},{j,n}]]; Join[{1},Array[a,10]]

a(n) = {matpermanent(matrix(n, n, i, j, binomial(n*i, j)))}; \\ Vaclav Kotesovec, Oct 08 2023

cp's OEIS Frontend

A120929 Partial sums of n^(n^2), A002489.

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A366355 a(n) = (-1)^n * QPochhammer(n, n, n).

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A366361 a(n) is the permanent of the n X n matrix M(n) defined by M[i, j, n] = binomial(n*i, j).

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