A173213 Column 2 of triangle A173210.

1, 9, 144, 6000, 537300, 83163780, 19475406720, 6361668149760, 2746842197022000, 1509038968593618000, 1025108190779715504000, 842146203249705132979200, 821879108168683849764480000

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..12.

Prog

(PARI) {a(n)=local(M=Mat(1), N, L, C=matrix(n+3, n+3, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n+2, 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+3, 3]}

Crossrefs

Cf. A173210, A173211, A173212, A173215 (row sums).

Sequence in context: A034829 A162993 A094594 * A223371 A046529 A331329

Adjacent sequences: A173210 A173211 A173212 * A173214 A173215 A173216

Keyword

nonn

Author

Paul D. Hanna, Feb 12 2010

Status

approved