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