OFFSET
0,2
COMMENTS
The numbers appear on the diagonal of a table T(n,k), where the left column contains the elements of A005563, and further columns are recursively T(n,k) = T(n,k-1)+T(n-1,k-1):
....0....-1.....0.....0.....0.....0.....0.....0.....0.....0.
....3.....3.....2.....2.....2.....2.....2.....2.....2.....2.
....8....11....14....16....18....20....22....24....26....28.
...15....23....34....48....64....82...102...124...148...174.
...24....39....62....96...144...208...290...392...516...664.
...35....59....98...160...256...400...608...898..1290..1806.
...48....83...142...240...400...656..1056..1664..2562..3852.
...63...111...194...336...576...976..1632..2688..4352..6914.
...80...143...254...448...784..1360..2336..3968..6656.11008.
...99...179...322...576..1024..1808..3168..5504..9472.16128.
..120...219...398...720..1296..2320..4128..7296.12800.22272.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
G.f.: x*(-3+4*x)/(2*x-1)^3. - R. J. Mathar, Dec 11 2010
a(n) = 2^(n-2)*n*(5+n). - R. J. Mathar, Dec 11 2010
a(n+1)-a(n) = A084266(n+1).
a(n+2) = 16*A058396(n) for n > 0.
a(n) = 2*a(n-1) + A001792(n).
a(n) = A001793(n) - 2^(n-1) for n > 0. - Brad Clardy, Mar 02 2012
a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} (k+3) * C(n-1,i). - Wesley Ivan Hurt, Sep 20 2017
From Amiram Eldar, Aug 13 2022: (Start)
Sum_{n>=1} 1/a(n) = 1322/75 - 124*log(2)/5.
Sum_{n>=1} (-1)^(n+1)/a(n) = 132*log(3/2)/5 - 782/75. (End)
MATHEMATICA
LinearRecurrence[{6, -12, 8}, {0, 3, 14}, 30] (* Harvey P. Dale, Oct 19 2015 *)
PROG
(Magma) [2^(n-2)*n*(5+n) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011
(PARI) a(n)=n*(n+5)<<(n-2) \\ Charles R Greathouse IV, Sep 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 06 2010
STATUS
approved