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A081107
7th binomial transform of (1,1,0,0,0,0,...).
3
1, 8, 63, 490, 3773, 28812, 218491, 1647086, 12353145, 92236816, 686011319, 5084554482, 37569208117, 276825744020, 2034669218547, 14920907602678, 109193914728689, 797590333670424, 5815762849680175, 42338753545671674, 307770170005074861, 2234183456333136028
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) + 6*m(i-1,j-1). - Benoit Cloitre, Jun 13 2003
FORMULA
a(n) = 14*a(n-1) - 49*a(n-2) with n > 1, a(0) = 1, a(1) = 8.
a(n) = (n + 7)*7^(n-1).
G.f.: (1 - 6*x)/(1 - 7*x)^2.
E.g.f.: exp(7*x)*(1 + x). - Stefano Spezia, Mar 05 2023
MATHEMATICA
CoefficientList[Series[(1 - 6 x)/(1 - 7 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
PROG
(Magma) [(n+7)*7^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 07 2003
STATUS
approved