A081109 9th binomial transform of (1,1,0,0,0,0,0,...).

1, 10, 99, 972, 9477, 91854, 885735, 8503056, 81310473, 774840978, 7360989291, 69735688020, 659002251789, 6213449802582, 58462914051567, 549043018919064, 5147278302366225, 48178524910147866, 450283905890997363

Offset: 0

Author

Paul Barry, Mar 07 2003

Keywords

• easy
• nonn

Comments

Main diagonal of array defined by m(0,j) = j; m(i,0) = i and m(i,j) = m(i-1,j) + 8*m(i-1,j-1). - Benoit Cloitre, Jun 13 2003

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (18, -81).

Crossrefs

Cf. A081108, A081122, A006234.

Programs

Magma

[(n+9)*9^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Mathematica

CoefficientList[Series[(1 - 8 x) / (1 - 9 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

Formula

a(n) = 18*a(n-1) - 81*a(n-2), a(0) = 1, a(1) = 10.

a(n) = (n + 9)*9^(n-1).

G.f.: (1 - 8*x)/(1 - 9*x)^2.

E.g.f.: exp(9*x)*(1 + x). - Stefano Spezia, Mar 04 2023