A275576 Sums of lengths of longest (strictly) increasing subsequences of all n^n length-n lists of integers from {1,2,...,n}.

1, 5, 45, 524, 7450, 125992, 2472197, 55163096, 1379215566, 38203654070, 1161476316583, 38452206880034, 1376997068182450, 53036098532973584, 2186272797635061105, 96043562430904351024, 4479387734051244791950, 221051522602427094486042

Offset: 1

Author

Jeffrey Shallit, Aug 02 2016

Keywords

• nonn
• more

Examples

			For n = 2 there are 4 such sequences:  (1,1), (1,2), (2,1), and (2,2).
The corresponding lengths of longest (strictly) increasing subsequences of these is 1, 2, 1, 1, so a(2) = 5.
		

Crossrefs

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

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

Cf. A245667.

Formula

a(n) = Sum_{k=1..n} k * A245667(n,k). - Alois P. Heinz, Nov 02 2018

Extensions

a(8)-a(18) from Alois P. Heinz, Nov 02 2018