A067403 Third column of triangle A067402.

1, 5, 45, 405, 3645, 32805, 295245, 2657205, 23914845, 215233605, 1937102445, 17433922005, 156905298045, 1412147682405, 12709329141645, 114383962274805, 1029455660473245, 9265100944259205, 83385908498332845, 750473176484995605, 6754258588364960445, 60788327295284644005

Offset: 0

Author

Wolfdieter Lang, Jan 25 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (9).

Crossrefs

Cf. A002001 (second column), A067404 (fourth column), A001019 (powers of 9).

Cf. A067402.

Programs

Maple

A067403:=n->5*9^(n-1): 1,seq(A067403(n), n=1..30); # Wesley Ivan Hurt, Apr 09 2017

Mathematica

Join[{1},NestList[9#&,5,30]] (* or *) CoefficientList[Series[ (1-4x)/ (1-9x),{x,0,30}],x] (* Harvey P. Dale, Apr 26 2011 *)

PARI

Vec((1-4*x)/(1-9*x) + O(x^30)) \\ Michel Marcus, Apr 09 2017

Formula

a(n) = A067402(n+2, 2).

a(n) = 5*9^(n-1) for n>=1, a(0) = 1.

G.f.: (1-4*x)/(1-9*x).

E.g.f.: (4 + 5*exp(9*x))/9. - Stefano Spezia, Sep 30 2022