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A248060 Sums over successive antidiagonals of A248059.

%I A248060 #29 Nov 23 2015 01:43:26
%S A248060 0,0,1,14,89,416,1526,4740,12898,31680,71527,150722,299571,566592,
%T A248060 1026524,1791528,3025188,4961280,7926621,12370710,18901069,28327904,
%U A248060 41716466,60451820,86313734,121567680,169068835,232386570,315945319,425191040,566777976,748786896
%N A248060 Sums over successive antidiagonals of A248059.
%H A248060 Christopher Hunt Gribble, <a href="/A248060/b248060.txt">Table of n, a(n) for n = 1..10000</a>
%F A248060 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.
%F A248060 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
%e A248060 a(1..9) are formed as follows:
%e A248060 .             Antidiagonals of A248059                   n    a(n)
%e A248060 .                         0                              1       0
%e A248060 .                      0     0                           2       0
%e A248060 .                   0     1     0                        3       1
%e A248060 .                1     6     6     1                     4      14
%e A248060 .             3    22    39    22     3                  5      89
%e A248060 .          9    60   139   139    60     9               6     416
%e A248060 .      19   135   371   476   371   135    19            7    1526
%e A248060 .   38   266   813  1253  1253   813   266    38         8    4740
%e A248060 .66   476  1574  2706  3254  2706  1574   476    66      9   12898
%p A248060 b := proc (n::integer, k::integer)::integer;
%p A248060   (4*k^4*n^4 - 24*k^3*n^3 + 2*k^4 + 12*k^3*n + 80*k^2*n^2 +
%p A248060    12*k*n^3 + 2*n^4 - 24*k^3 - 24*k^2*n - 24*k*n^2 - 24*n^3 +
%p A248060    40*k^2 - 102*k*n + 40*n^2 + 9 + (- 2*k^4 - 12*k^3*n + 24*k^3 +
%p A248060    24*k^2*n - 40*k^2 + 6*k*n - 9)*(-1)^n + (- 12*k*n^3 - 2*n^4 +
%p A248060    24*k*n^2 + 24*n^3 + 6*k*n - 40*n^2 - 9)*(-1)^k +
%p A248060    (- 6*k*n + 9)*(-1)^k*(-1)^n)/384
%p A248060 end proc;
%p A248060 for j to 40 do a := 0;
%p A248060   for k from j by -1 to 1 do
%p A248060     n := j-k+1;
%p A248060     a := a+b(n, k);
%p A248060   end do;
%p A248060   printf("%d, ", a):
%p A248060 end do:
%Y A248060 Cf. A248059.
%K A248060 nonn
%O A248060 1,4
%A A248060 _Christopher Hunt Gribble_, Sep 30 2014
%E A248060 Terms corrected and extended by _Christopher Hunt Gribble_, Apr 06 2015