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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Antidiagonal sums are in A136396.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,0) = 1; T(n,k) = n*(2+n*(k-1)), k > 0. - R. J. Mathar, Jan 05 2011

EXAMPLE

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.

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

CROSSREFS

Cf. A136396, A179901.

Sequence in context: A305540 A197871 A093010 * A210559 A180803 A093966

Adjacent sequences:  A178997 A178998 A178999 * A179001 A179002 A179003

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jan 03 2011

STATUS

approved

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Last modified September 20 16:31 EDT 2020. Contains 337265 sequences. (Running on oeis4.)