A159640 - OEIS

%I #13 Feb 10 2022 20:31:17

%S 1,1,3,18,234,7020,498420,84731400,34655142600,34169970603600,

%T 81290360065964400,466769247498767584800,6469888539580417492912800,

%U 216495410311439930147848113600,17489148731189051877133614160948800,3410838720448876031389860235353200668800

%N a(1) = a(2) = 1; for n > 2, a(n) = (a(1), a(2), a(3), ...) dot (P(1), P(2), P(3), ...); P = A000129.

%C The sequence starting (1, 3, 18, ...) = the eigensequence of an infinite lower triangular matrix with n terms of the Pell series in each row: (1, 2, 5, ...).

%F a(1) = 1, a(2) = 1, then a(n) = Sum_{j=1..n-1} a(j)*A000129(j), for n >2.

%e a(5) = 234 = (1, 1, 3, 18) dot (1, 2, 5, 12) = (1 + 2 + 15 + 216).

%p A159640 := proc(n)

%p     option remember;

%p     if n <= 2 then

%p         1;

%p     else

%p         add(procname(j)*A000129(j),j=1..n-1) ;

%p     end if;

%p end proc: # _R. J. Mathar_, Aug 12 2012

%o (PARI) P(n) = ([2, 1; 1, 0]^n)[2, 1]; \\ A000129

%o a(n) = if (n>2, sum(j=1, n-1, a(j)*P(j)), 1); \\ _Michel Marcus_, Feb 09 2022

%Y Cf. A000129.

%K nonn

%O 1,3

%A _Gary W. Adamson_, Apr 18 2009