OFFSET
0,2
COMMENTS
Binomial transform of A050407, (starting with 1,1,1,2,5,...). 2nd binomial transform of (1,0,0,1,0,0,0,0,...). Case k=2 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f. (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..225
Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
FORMULA
a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48.
G.f.: (1 - 6x + 12x^2 - 7x^3)/(1-2x)^4.
PROG
(Magma) [2^n*(n^3-3*n^2+2*n+48)/48: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved