A173211 Column 0 of triangle A173210.

1, 1, 4, 84, 4584, 469440, 76982940, 18391183020, 6011375932800, 2570927357779200, 1391371186976089200, 928454707768609098000, 748225283395263813216000, 715960677236011729384262400

Offset

0,3

Comments

Triangle T = A173210 satisfies: row n of T^n = row n of (I+D)^(n^2) where D is the lower diagonal matrix: D(n+1,n)=n+1.

Links

Table of n, a(n) for n=0..13.

Prog

(PARI) {a(n)=local(M=Mat(1), N, L, C=matrix(n+1, n+1, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n, N=M; M=matrix(#N+1, #N+1, r, c, if(r>=c, if(r<=#N, (N^(#N))[r, c], (C^((#M)^2))[r, c]))); L=sum(i=1, #M, -(M^0-M)^i/i); M=sum(i=0, #M, (L/#N)^i/i!); ); M[n+1, 1]}

Crossrefs

Cf. A173210, A173212, A173213.

Sequence in context: A012107 A012189 A012076 * A109901 A367522 A015018

Adjacent sequences: A173208 A173209 A173210 * A173212 A173213 A173214

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2010

Status

approved