A076483 -id:A076483 - cp's OEIS frontend

A076482 Triangle with T(n,k)=n!*(k-1)^k/k! where 1<=k<=n.

0, 0, 1, 0, 3, 8, 0, 12, 32, 81, 0, 60, 160, 405, 1024, 0, 360, 960, 2430, 6144, 15625, 0, 2520, 6720, 17010, 43008, 109375, 279936, 0, 20160, 53760, 136080, 344064, 875000, 2239488, 5764801, 0, 181440, 483840, 1224720, 3096576, 7875000, 20155392, 51883209, 134217728

Offset: 1

Henry Bottomley, Oct 14 2002

			Rows start
  0;
  0,   1;
  0,   3,   8;
  0,  12,  32,   81;
  0,  60, 160,  405, 1024;
  0, 360, 960, 2430, 6144, 15625;
  ...

Seiichi Manyama, Rows n = 1..140, flattened

Row sums are A076483.

Cf. A001710, A007778, A008279.

Table[n! (k-1)^k/k!,{n,0,10},{k,n}]//Flatten (* Harvey P. Dale, Nov 28 2019 *)

T(n,k) = n*T(n, k-1) = A007778(k-1)*A008279(n,n-k) starting with T(n,n) = (n-1)^n = A007778(n-1).

A076630 a(n) is the smallest number such that product of first n terms is strictly greater than n-th power of a(n-1) starting with a(1)=1.

Original entry on oeis.org

1, 2, 5, 63, 1575297, 15398261127422599513389116979

Offset: 1

Henry Bottomley, Oct 22 2002

nonn

Next term is 1.343...*10^160. Of the n^n ways of selecting n terms from {a(1),a(2),...,a(n)}, n!*Sum_k{1<=k<=n}(k-1)^k/k!=A076483(n) ways have a product strictly less than a(1)*a(2)*...*a(n) and this is possibly the smallest sequence with that property. If the definition had been: a(n) is the smallest number such that sum of first n terms is greater than n times a(n-1) starting with a(1)=1, then the resulting sequence would have been A003422.

			a(4)=1+floor[5^4/(1*2*5)]=1+floor[62.5]=63.

Cf. A076483.

a(n) = 1 + floor[a(n-1)^n / Product_i{0

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A076482 Triangle with T(n,k)=n!*(k-1)^k/k! where 1<=k<=n.

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