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A051846 Digits 1..n in strict descending order n..1 interpreted in base n+1.

%I A051846 #49 Apr 04 2024 10:04:25
%S A051846 1,7,57,586,7465,114381,2054353,42374116,987654321,25678050355,
%T A051846 736867805641,23136292864686,789018236134297,29043982525261081,
%U A051846 1147797409030816545,48471109094902544776,2178347851919531492065,103805969587115219182431
%N A051846 Digits 1..n in strict descending order n..1 interpreted in base n+1.
%C A051846 All odd-indexed (2n+1) terms are divisible by (2n+1). See A051847.
%C A051846 All even-indexed (2n) terms are divisible by n. - _Alexander R. Povolotsky_, Oct 20 2022
%H A051846 Alois P. Heinz, <a href="/A051846/b051846.txt">Table of n, a(n) for n = 1..200</a>
%H A051846 Chai Wah Wu, <a href="https://arxiv.org/abs/2403.20304">Pandigital and penholodigital numbers</a>, arXiv:2403.20304 [math.GM], 2024. See p. 1.
%F A051846 a(n) = Sum_{i=1..n} i*(n+1)^(i-1).
%F A051846 a(n) = ((n+1)^(n+1)*(n-1) + 1)/n^2 = A062806(n+1)/(n+1) - (n+1)^(n+1). - _Benoit Cloitre_, Sep 28 2002
%F A051846 a(n) = A028310(n-1) * A023811(n+1) + A199969(n+1). - _M. F. Hasler_, Jan 22 2013
%F A051846 a(n) = (n-1) * A058128(n+1) + 1. - _Seiichi Manyama_, Apr 10 2022
%e A051846 a(1) = 1,
%e A051846 a(2) = 2*3 + 1 = 7,
%e A051846 a(3) = 3*(4^2) + 2*4 + 1 = 57,
%e A051846 a(4) = 4*(5^3) + 3*(5^2) + 2*5 + 1 = 586.
%p A051846 a(n) := proc(n) local i; add(i*((n+1)^(i-1)),i=1..n); end;
%t A051846 Array[Sum[i*(# + 1)^(i - 1), {i, #}] &, 18] (* _Michael De Vlieger_, Apr 04 2024 *)
%o A051846 (PARI) a(n)=((n+1)^(n+1)*(n-1)+1)/n^2
%o A051846 (Maxima) makelist(((n+1)^(n+1)*(n-1) + 1)/n^2,n,1,20); /* _Martin Ettl_, Jan 25 2013 */
%o A051846 (Python)
%o A051846 def a(n): return sum((i+1)*(n+1)**i for i in range(n))
%o A051846 print([a(n) for n in range(1, 20)]) # _Michael S. Branicky_, Apr 10 2022
%Y A051846 The right edge of A051845.
%Y A051846 Cf. A023811, A051847, A058128, A062806, A199969.
%K A051846 easy,base,nonn
%O A051846 1,2
%A A051846 _Antti Karttunen_, Dec 13 1999
%E A051846 Minor edits in formulas by _M. F. Hasler_, Oct 11 2019