A132872 - OEIS

%I #23 Mar 08 2020 22:50:35

%S 1,1,6,132,7156,729895,119636226,28619359629,9374688646296,

%T 4019108763468573,2180474045020534600,1458451073246597456521,

%U 1177921104348705716833164,1129393220849450436646366223,1267471534789127127256106086245

%N Column 0 of triangle A132870 (first 30 terms only).

%C Triangle T = A132870 obeys: the g.f. of row n of T^n = (y + n^2)^n for n >= 0.

%C This yields non-integer values for n = 30, 31, 62, 63, 94, 95, ..., so the integer sequence ends at n = 29.

%H Jinyuan Wang, <a href="/A132872/b132872.txt">Table of n, a(n) for n = 0..29</a>

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

%o (PARI) A132872(n)=T(n,0) \\ with T(.) from A132870. The code above is very inefficient.

%o A132872_vec(N)=T(N)[,1] \\ compute all terms a(0..N) at once, in the same time as required for computing only a(N). - _M. F. Hasler_, Nov 19 2017

%Y Cf. A132870, A132871, A132873.

%K nonn,fini,full

%O 0,3

%A _Paul D. Hanna_, Sep 29 2007

%E Edited by _M. F. Hasler_, Nov 22 2017

%E b-file with non-integral entries deleted by _N. J. A. Sloane_, Mar 02 2018