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A062813 a(n) = Sum_{i=0..n-1} i*n^i. 12
0, 2, 21, 228, 2930, 44790, 800667, 16434824, 381367044, 9876543210, 282458553905, 8842413667692, 300771807240918, 11046255305880158, 435659737878916215, 18364758544493064720, 824008854613343261192, 39210261334551566857170, 1972313422155189164466189, 104567135734072022160664820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Largest Katadrome (number with digits in strict descending order) in base n.

The largest permutational number (A134640) of order n. These numbers are isomorphic with antidiagonal permutation matrices of order n. Where diagonal matrices are a[i,1+n-i]=1 {i=1,n} a[i<>1+n-i]=0 for smallest permutational numbers of order n see A023811. - Artur Jasinski, Nov 07 2007

Permutational numbers A134640 isomorphic with permutation matrix generators of cyclic groups, n-th root of unity matrices. - Artur Jasinski, Nov 07 2007

a(n) = A134640(n,A000142(n)). - Reinhard Zumkeller, Aug 29 2014

Rephrasing: Largest pandigital number in base n (in the sense of A050278, which is base 10); e.g., a(10) = A050278(3265920), its final term. With a(1) = 1 instead of 0, also accommodates unary (A000042). - Rick L. Shepherd, Jul 10 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..400

FORMULA

a(n) = n^n - (n^n-n)/(n-1)^2 for n>1. - Dean Hickerson, Jun 26 2001

MAPLE

0, seq(n*((n-2)*n^n + 1)/(n-1)^2, n=2..100); # Robert Israel, Sep 03 2014

MATHEMATICA

Table[Sum[i*n^i, {i, 0, -1 + n}], {n, 17}] (* Olivier Gérard, Jun 23 2001 *)

a[n_] := FromDigits[ Range[ n-1, 0, -1], n]; Array[a, 18] (* Robert G. Wilson v, Sep 03 2014 *)

PROG

(PARI) a(n) = sum(i=0, n-1, i*n^i)

(PARI) a(n) = if (n==1, 0, my(t=n^n); t-(t-n)/(n-1)^2); \\ Joerg Arndt, Sep 03 2014

(Haskell)

a062813 n = foldr (\dig val -> val * n + dig) 0 [0 .. n - 1]

-- Reinhard Zumkeller, Aug 29 2014

CROSSREFS

Cf. A134640, A134641, A134642, A134643, A134644, A023811, A062808.

Cf. A000142, A000042, A050278.

Sequence in context: A058476 A099748 A023812 * A024231 A069717 A036679

Adjacent sequences:  A062810 A062811 A062812 * A062814 A062815 A062816

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Jun 23 2001

STATUS

approved

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)