OFFSET
0,2
COMMENTS
Binomial transform of A000124 (when this begins 1,1,2,4,7,...).
2nd binomial transform of (1,0,1,0,0,0,...).
Case k=2 where a(n,k) = k^n(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
G.f.: (1 - 4*x + 5*x^2)/(1-2*x)^3.
a(n) = Sum_{k=0..n} C(n, k)*(1 + C(k, 2)). - Paul Barry, May 27 2003
E.g.f.: (2 + x^2)*exp(2*x)/2. - G. C. Greubel, Oct 17 2018
MATHEMATICA
Table[2^n*(n^2-n+8)/8, {n, 0, 50}] (* or *) LinearRecurrence[{6, -12, 8}, {1, 2, 5}, 50] (* G. C. Greubel, Oct 17 2018 *)
PROG
(Magma) [2^n*(n^2-n+8)/8: n in [0..40]]; Vincenzo Librandi, Apr 27 2011
(PARI) a(n)=2^n*(n^2-n+8)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved