A033463 EXPCONV of squares A000290 with themselves.

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

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

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

Adjacent sequences: A033460 A033461 A033462 * A033464 A033465 A033466

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Aug 27 2014

Status

approved