A275576 - OEIS

A275576

Sums of lengths of longest (strictly) increasing subsequences of all n^n length-n lists of integers from {1,2,...,n}.

%I #15 Nov 02 2018 22:52:24

%S 1,5,45,524,7450,125992,2472197,55163096,1379215566,38203654070,

%T 1161476316583,38452206880034,1376997068182450,53036098532973584,

%U 2186272797635061105,96043562430904351024,4479387734051244791950,221051522602427094486042

%N Sums of lengths of longest (strictly) increasing subsequences of all n^n length-n lists of integers from {1,2,...,n}.

%F a(n) = Sum_{k=1..n} k * A245667(n,k). - _Alois P. Heinz_, Nov 02 2018

%e For n = 2 there are 4 such sequences: (1,1), (1,2), (2,1), and (2,2).

%e The corresponding lengths of longest (strictly) increasing subsequences of these is 1, 2, 1, 1, so a(2) = 5.

%Y Cf. A003316, which computes the same thing for permutations.

%Y Cf. A275577, which computes the same thing for not necessarily strictly increasing subsequences.

%Y Cf. A245667.

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Aug 02 2016

%E a(8)-a(18) from _Alois P. Heinz_, Nov 02 2018