A136396 a(n) = 1 + n*(n+1)*(n^2-n+12)/12.

1, 3, 8, 19, 41, 81, 148, 253, 409, 631, 936, 1343, 1873, 2549, 3396, 4441, 5713, 7243, 9064, 11211, 13721, 16633, 19988, 23829, 28201, 33151, 38728, 44983, 51969, 59741, 68356, 77873, 88353, 99859, 112456, 126211, 141193, 157473, 175124, 194221, 214841, 237063, 260968, 286639

Offset: 0

Author

Gary W. Adamson, Dec 29 2007

Keywords

• nonn
• easy

Comments

Equals antidiagonal sums of the array A179000.

Examples

			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).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A001263, A007318, A179000.

Programs

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 *)

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