A252766 a(n) = n-th number of the n-th iteration of the hyperbinomial transform on the sequence of 1's.
1, 2, 13, 163, 2993, 71801, 2120545, 74300269, 3010775745, 138473150833, 7125155956601, 405508439303573, 25289672996300113, 1715033239186419673, 125649446059365470481, 9889850149432716471301, 832278360169843776972545, 74571018189601103968946273
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..350
Crossrefs
Main diagonal of A144303.
Programs
-
Maple
a:= n-> `if`(n=0, 1, add(n*(2*n-j)^(n-j-1)*binomial(n, j), j=0..n)): seq(a(n), n=0..20);
Formula
a(n) = Sum_{j=0..n} n * (2*n-j)^(n-j-1) * C(n,j) for n>0, a(0) = 1.