A159640 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.

1, 1, 3, 18, 234, 7020, 498420, 84731400, 34655142600, 34169970603600, 81290360065964400, 466769247498767584800, 6469888539580417492912800, 216495410311439930147848113600, 17489148731189051877133614160948800, 3410838720448876031389860235353200668800

Offset

1,3

Comments

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, ...).

Links

Table of n, a(n) for n=1..16.

Formula

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

Example

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

Maple

A159640 := proc(n)
    option remember;
    if n <= 2 then
        1;
    else
        add(procname(j)*A000129(j), j=1..n-1) ;
    end if;
end proc: # R. J. Mathar, Aug 12 2012

Prog

(PARI) P(n) = ([2, 1; 1, 0]^n)[2, 1]; \\ A000129
a(n) = if (n>2, sum(j=1, n-1, a(j)*P(j)), 1); \\ Michel Marcus, Feb 09 2022

Crossrefs

Cf. A000129.

Sequence in context: A195763 A265460 A137223 * A038061 A232916 A327231

Adjacent sequences: A159637 A159638 A159639 * A159641 A159642 A159643

Keyword

nonn

Author

Gary W. Adamson, Apr 18 2009

Status

approved