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A081109
9th binomial transform of (1,1,0,0,0,0,0,...).
4
1, 10, 99, 972, 9477, 91854, 885735, 8503056, 81310473, 774840978, 7360989291, 69735688020, 659002251789, 6213449802582, 58462914051567, 549043018919064, 5147278302366225, 48178524910147866, 450283905890997363
OFFSET
0,2
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
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
MATHEMATICA
CoefficientList[Series[(1 - 8 x) / (1 - 9 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
PROG
(Magma) [(n+9)*9^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 07 2003
STATUS
approved