A179000 Array T(n,k) read by antidiagonals: coefficient [x^k] of (1 + n*Sum_{i>=1} x^i)^2, k >= 0.
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, 14, 48, 60, 56, 42, 24, 8, 1, 16, 63, 84, 85, 72, 51, 28, 9, 1, 18, 80, 112, 120, 110, 88, 60, 32, 10
Offset: 1
Examples
First few rows of the array: 1 2 3 4 5 6 7 8 9 10 11 A000027 1 4 8 12 16 20 24 28 32 36 40 A008574 1 6 15 24 33 42 51 60 69 78 87 A122709 1 8 24 40 56 72 88 104 120 136 152 A051062 1 10 35 60 85 110 135 160 185 210 235 1 12 48 84 120 156 192 228 264 300 336 1 14 63 112 161 210 259 308 357 406 455 1 16 80 144 208 272 336 400 464 528 592 1 18 99 180 261 342 423 504 585 666 747 Row n=3 is generated by (1 + 3x + 3x^2 + 3x^3 + 3x^4 + ...)^2 = 1 + 6x + 15x^2 + 24x^3 + ..., for example.
Programs
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Maple
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
Formula
T(n,0) = 1; T(n,k) = n*(2+n*(k-1)), k > 0. - R. J. Mathar, Jan 05 2011
Comments