A248060 Sums over successive antidiagonals of A248059.

0, 0, 1, 14, 89, 416, 1526, 4740, 12898, 31680, 71527, 150722, 299571, 566592, 1026524, 1791528, 3025188, 4961280, 7926621, 12370710, 18901069, 28327904, 41716466, 60451820, 86313734, 121567680, 169068835, 232386570, 315945319, 425191040, 566777976, 748786896

Offset: 1

Author

Christopher Hunt Gribble, Sep 30 2014

Keywords

• nonn

Examples

			a(1..9) are formed as follows:
.             Antidiagonals of A248059                   n    a(n)
.                         0                              1       0
.                      0     0                           2       0
.                   0     1     0                        3       1
.                1     6     6     1                     4      14
.             3    22    39    22     3                  5      89
.          9    60   139   139    60     9               6     416
.      19   135   371   476   371   135    19            7    1526
.   38   266   813  1253  1253   813   266    38         8    4740
.66   476  1574  2706  3254  2706  1574   476    66      9   12898
		

Links

• Christopher Hunt Gribble, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A248059.

Programs

Maple

b := proc (n::integer, k::integer)::integer;
  (4*k^4*n^4 - 24*k^3*n^3 + 2*k^4 + 12*k^3*n + 80*k^2*n^2 +
   12*k*n^3 + 2*n^4 - 24*k^3 - 24*k^2*n - 24*k*n^2 - 24*n^3 +
   40*k^2 - 102*k*n + 40*n^2 + 9 + (- 2*k^4 - 12*k^3*n + 24*k^3 +
   24*k^2*n - 40*k^2 + 6*k*n - 9)*(-1)^n + (- 12*k*n^3 - 2*n^4 +
   24*k*n^2 + 24*n^3 + 6*k*n - 40*n^2 - 9)*(-1)^k +
   (- 6*k*n + 9)*(-1)^k*(-1)^n)/384
end proc;
for j to 40 do a := 0;
  for k from j by -1 to 1 do
    n := j-k+1;
    a := a+b(n, k);
  end do;
  printf("%d, ", a):
end do:

Formula

Empirically, a(n) = (2*n^9 + 18*n^8 + 18*n^7 - 210*n^6 + 588*n^5 + 672*n^4 - 3803*n^3 - 1425*n^2 + 3195*n + 945 + 315*n^3*(-1)^n + 945*n^2*(-1)^n - 315*n*(-1)^n - 945*(-1)^n)/120960.

Empirical g.f.: x^3*(x^8-4*x^6+8*x^5+26*x^4+40*x^3+16*x^2+8*x+1) / ((x-1)^10*(x+1)^4). - Colin Barker, Apr 08 2015

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 06 2015