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

Author

Alois P. Heinz, Dec 21 2014

Keywords

• nonn

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.