A173212 Column 1 of triangle A173210.

1, 4, 36, 1056, 73200, 9179640, 1794887640, 500614248960, 187826632116480, 90939137506660800, 55080912083696452800, 40741241351161144147200, 36096696228114024645542400, 37707879201499850798028974400

Offset

0,2

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+2, n+2, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n+1, 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+2, 2]}

Crossrefs

Cf. A173210, A173211, A173213.

Sequence in context: A337851 A353410 A360725 * A371611 A143764 A152287

Adjacent sequences: A173209 A173210 A173211 * A173213 A173214 A173215

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2010

Status

approved