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A033463 EXPCONV of squares A000290 with themselves. 1
1, 8, 50, 248, 1048, 3952, 13696, 44480, 137216, 406016, 1160704, 3223552, 8734720, 23171072, 60342272, 154615808, 390529024, 973864960, 2400845824, 5857869824, 14159446016, 33935065088, 80698408960, 190534647808, 446911479808, 1041898668032, 2415348678656, 5570035712000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 2^(n-4)*(n^4+6*n^3+19*n^2+22*n+16). E.g.f.: (1+3*x+x^2)^2*exp(2*x). O.g.f.: (1-2*x+10*x^2-12*x^3+8*x^4)/(1-2*x)^5. Recurrence: a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5). a(n) = Sum_{k=0..n} binomial(n, k)*(k+1)^2*(n-k+1)^2. - Vladeta Jovovic, Sep 17 2003
MATHEMATICA
LinearRecurrence[{10, -40, 80, -80, 32}, {1, 8, 50, 248, 1048}, 30] (* Harvey P. Dale, Aug 26 2014 *)
CoefficientList[Series[(1 - 2 x + 10 x^2 - 12 x^3 + 8 x^4)/(1 - 2 x)^5, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 27 2014 *)
PROG
(Magma) I:=[1, 8, 50, 248, 1048]; [n le 5 select I[n] else 10*Self(n-1)-40*Self(n-2)+80*Self(n-3)-80*Self(n-4)+32*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Aug 27 2014
CROSSREFS
Sequence in context: A300318 A290617 A163228 * A030279 A133357 A081675
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Aug 27 2014
STATUS
approved

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Last modified February 23 20:31 EST 2024. Contains 370288 sequences. (Running on oeis4.)