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A081041 6th binomial transform of (1,5,0,0,0,0,0,0,...). 3
1, 11, 96, 756, 5616, 40176, 279936, 1912896, 12877056, 85660416, 564350976, 3688436736, 23944605696, 154551545856, 992612745216, 6347497291776, 40435908673536, 256721001578496, 1624959306694656, 10257555623510016 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 67.
FORMULA
a(n) = 12*a(n-1) - 36*a(n-2) for n>1, a(0)=1, a(1)=9.
a(n) = (5*n+6)*6^(n-1).
a(n) = Sum_{k=0..n} (k+1)*5^k*binomial(n, k).
G.f.: (1-x)/(1-6x)^2.
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - 6 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12, -36}, {1, 11}, 20] (* Harvey P. Dale, Mar 04 2019 *)
PROG
(Magma) [(5*n+6)*6^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
CROSSREFS
Sequence in context: A051446 A271632 A055286 * A294724 A115351 A154997
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 04 2003
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)