A085388 - OEIS

A085388

First differences of n^k.

1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 18, 8, 0, 1, 5, 20, 48, 54, 16, 0, 1, 6, 30, 100, 192, 162, 32, 0, 1, 7, 42, 180, 500, 768, 486, 64, 0, 1, 8, 56, 294, 1080, 2500, 3072, 1458, 128, 0, 1, 9, 72, 448, 2058, 6480, 12500, 12288, 4374, 256, 0, 1, 10, 90, 648

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

COMMENTS

T(n,k) is the number of k-digit numbers in base n; n,k >= 2. - Mohammed Yaseen, Nov 11 2022

LINKS

Table of n, a(n) for n=1..70.

FORMULA

T(n,k) = (n-1)*n^(k-1) + 0^k/n. - Corrected by Mohammed Yaseen, Nov 11 2022

T(n,0) = 1; T(n,k) = n^k - n^(k-1) for k >= 1. - Mohammed Yaseen, Nov 11 2022

EXAMPLE

Rows begin

1, 0, 0, 0, 0, ...

1, 1, 2, 4, 8, ...

1, 2, 6, 18, 54, ...

1, 3, 12, 48, 192, ...

1, 4, 20, 100, 500, ...

CROSSREFS

Rows include A011782, A025192, A002001, A005054, A052934, A055272, A055274, A055275, A052268, A055276.

Diagonals include A053506, A085389, A085390.

Row-wise binomial transform is A083064.

Sequence in context: A246935 A342120 A198793 * A351339 A361432 A294498

Adjacent sequences: A085385 A085386 A085387 * A085389 A085390 A085391

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jun 30 2003

EXTENSIONS

Offset corrected by Mohammed Yaseen, Nov 11 2022

STATUS

approved