OFFSET
0,2
COMMENTS
Equals antidiagonal sums of the array A179000.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
A007318 * [1,2,3,2,0,0,0,...]: Binomial transform of [1, 2, 3, 3, 2, 0, 0, 0, ...].
Narayana transform of [1,2,1,0,0,0,...]: (A001263) * [1, 2, 1, 0, 0, 0, ...].
G.f.: ( -1+2*x-3*x^2+x^3-x^4 ) / (x-1)^5. - R. J. Mathar, Jan 05 2011
EXAMPLE
a(3) = 19 = (1, 3, 3, 1) dot (1, 2, 3, 3) = (1 + 6 + 9 + 3).
a(3) = 19 = (1, 6, 6, 1) dot (1, 2, 1, 0) = (1 + 12 + 6 + 0), where (1, 6, 6, 1) = row 4 of the Narayana triangle (A001263).
MAPLE
A136396 := proc(n) 1+n*(n+1)*(n^2-n+12)/12 ; end proc:
MATHEMATICA
Table[1+n(n+1)(n^2-n+12)/12, {n, 0, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 8, 19, 41}, 50] (* Harvey P. Dale, Feb 06 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 29 2007
STATUS
approved