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A179000 Array T(n,k) read by antidiagonals: coefficient [x^k] of (1 + n*Sum_{i>=1} x^i)^2, k >= 0.

%I A179000 #11 Jan 06 2019 03:58:30
%S A179000 1,1,2,1,4,3,1,6,8,4,1,8,15,12,5,1,10,24,24,16,6,1,12,35,40,33,20,7,1,
%T A179000 14,48,60,56,42,24,8,1,16,63,84,85,72,51,28,9,1,18,80,112,120,110,88,
%U A179000 60,32,10
%N A179000 Array T(n,k) read by antidiagonals: coefficient [x^k] of (1 + n*Sum_{i>=1} x^i)^2, k >= 0.
%C A179000 Antidiagonal sums are in A136396.
%F A179000 T(n,0) = 1; T(n,k) = n*(2+n*(k-1)), k > 0. - _R. J. Mathar_, Jan 05 2011
%e A179000 First few rows of the array:
%e A179000   1   2   3   4   5   6   7   8   9  10  11  A000027
%e A179000   1   4   8  12  16  20  24  28  32  36  40  A008574
%e A179000   1   6  15  24  33  42  51  60  69  78  87  A122709
%e A179000   1   8  24  40  56  72  88 104 120 136 152  A051062
%e A179000   1  10  35  60  85 110 135 160 185 210 235
%e A179000   1  12  48  84 120 156 192 228 264 300 336
%e A179000   1  14  63 112 161 210 259 308 357 406 455
%e A179000   1  16  80 144 208 272 336 400 464 528 592
%e A179000   1  18  99 180 261 342 423 504 585 666 747
%e A179000 Row n=3 is generated by (1 + 3x + 3x^2 + 3x^3 + 3x^4 + ...)^2 = 1 + 6x + 15x^2 + 24x^3 + ..., for example.
%p A179000 A179000 := proc(n,k) if k = 0 then 1; else 2*n+n^2*(k-1) ; end if; end proc: # _R. J. Mathar_, Jan 05 2011
%Y A179000 Cf. A136396, A179901.
%K A179000 nonn,tabl,easy
%O A179000 1,3
%A A179000 _Gary W. Adamson_, Jan 03 2011