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A321003
a(n) = 2^n*(4*3^n-1).
2
3, 22, 140, 856, 5168, 31072, 186560, 1119616, 6718208, 40310272, 241863680, 1451186176, 8707125248, 52242767872, 313456640000, 1880739905536, 11284439564288, 67706637647872, 406239826411520, 2437438959517696, 14624633759203328, 87747802559414272
OFFSET
0,1
COMMENTS
Conjectured to be the sum of A175046(i) for 1 <= i < 2^(n+1).
FORMULA
From Colin Barker, Nov 02 2018: (Start)
G.f.: (3 - 2*x) / ((1 - 2*x)*(1 - 6*x)).
a(n) = 8*a(n-1) - 12*a(n-2) for n>1.
(End)
E.g.f.: -exp(2*x)+4*exp(6*x). - Stefano Spezia, Nov 02 2018
MAPLE
a := n -> 2^n*(4*3^n-1):
seq(a(n), n = 0 .. 25); # Stefano Spezia, Nov 02 2018
MATHEMATICA
a[n_]:=2^n*(4*3^n-1); Array[a, 25, 0] (* or *)
CoefficientList[Series[-E^(2 x) + 4 E^(6 x), {x, 0, 25}], x]*Table[k!, {k, 0, 25}] (* Stefano Spezia, Nov 02 2018 *)
PROG
(PARI) Vec((3 - 2*x) / ((1 - 2*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Nov 02 2018
(PARI) a(n) = 2^n*(4*3^n-1); \\ Michel Marcus, Nov 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 01 2018
STATUS
approved