A248027 Sum over each antidiagonal of A248017.

0, 0, 0, 4, 69, 554, 3100, 13288, 47492, 147050, 407568, 1030912, 2419025, 5324684, 11099416, 22065120, 42085344, 77378556, 137705904, 237996060, 400624581, 658434694, 1058839380, 1669118984, 2583424948, 3931632406, 5890783808, 8699293304, 12674960961

Offset: 1

Author

Christopher Hunt Gribble, Sep 30 2014

Keywords

• nonn

Examples

			a(1)..a(9) are formed as follows:
.             Antidiagonals of A248017                 n   a(n)
.                         0                             1      0
.                      0     0                          2      0
.                   0     0     0                       3      0
.                0     2     2     0                    4      4
.             1    14    39    14     1                 5     69
.          3    66   208   208    66     3              6    554
.      12   198   794  1092   794   198    12           7   3100
.   28   508  2196  3912  3912  2196   508    28        8  13288
.66  1092  5231 10626 13462 10626  5231  1092    66     9  47492
		

Links

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

Crossrefs

Cf. A248017.

Programs

Maple

b := proc (n::integer, k::integer)::integer;
  (4*k^5*n^5 - 40*k^4*n^4 + 140*k^3*n^3 + 2*k^5 + 20*k^4*n
   + 30*k^3*n^2 + 30*k^2*n^3 + 20*k*n^4 + 2*n^5 - 40*k^4
   - 120*k^3*n - 185*k^2*n^2 - 120*k*n^3 - 40*n^4 + 160*k^3
   - 20*k^2*n - 20*k*n^2 + 160*n^3 - 80*k^2 + 36*k*n - 80*n^2
   + 48*k + 48*n + 45
   + (- 30*k^2*n^3 - 20*k*n^4 - 2*n^5 - 15*k^2*n^2 + 120*k*n^3
      + 40*n^4 + 20*k*n^2 - 160*n^3 + 60*k*n + 80*n^2 - 48*n
      - 45)*(-1)^k
   + (- 2*k^5 - 20*k^4*n - 30*k^3*n^2 + 40*k^4 + 120*k^3*n
      - 15*k^2*n^2 - 160*k^3 + 20*k^2*n + 80*k^2 + 60*k*n - 48*k
      - 45)*(-1)^n
   + (15*k^2*n^2 - 60*k*n + 45)*(-1)^k*(-1)^n)/1920;
end proc;
for j to 10000 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^11 + 22*n^10 + 22*n^9 - 462*n^8 - 1122*n^7 + 7392*n^6 - 3509*n^5 - 25663*n^4 + 48950*n^3 - 22869*n^2 - 65133*n + 41580 - (693*n^5 + 3465*n^4 - 6930*n^3 - 45045*n^2 + 27027*n + 41580)*(-1)^n)/2661120.

Empirical g.f.: -x^4*(x^11 + 2*x^10 - 7*x^9 - 10*x^8 - 28*x^7 - 170*x^6 - 484*x^5 - 538*x^4 - 461*x^3 - 176*x^2 - 45*x - 4) / ((x - 1)^12*(x + 1)^6). - Colin Barker, Apr 21 2015

Extensions

Terms corrected and extended by Christopher Hunt Gribble, Apr 17 2015