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A016161
Expansion of g.f. 1/((1-5*x)*(1-7*x)).
5
1, 12, 109, 888, 6841, 51012, 372709, 2687088, 19200241, 136354812, 964249309, 6798573288, 47834153641, 336059778612, 2358521965909, 16540171339488, 115933787267041, 812299450322412, 5689910849522509
OFFSET
0,2
COMMENTS
Also, this is the number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes each of shape 4k + 1. Cf. A003462, A109021. - R. K. Guy, Jan 31 2007
FORMULA
From R. J. Mathar, Sep 18 2008: (Start)
a(n) = (7^(n+1)-5^(n+1))/2 = A081200(n+1).
Binomial transform of A080962. (End)
a(n) = 7*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011
E.g.f.: exp(5*x)*(7*exp(2*x) - 5)/2. - Stefano Spezia, Oct 25 2023
MATHEMATICA
CoefficientList[Series[1/((1-5x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {12, -35}, {1, 12}, 30] (* Harvey P. Dale, Nov 16 2021 *)
PROG
(PARI) Vec(1/((1-5*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved