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A099233 Square array read by antidiagonals associated to sections of 1/(1-x-x^k). 5
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 5, 1, 1, 1, 5, 10, 13, 8, 1, 1, 1, 6, 15, 26, 28, 13, 1, 1, 1, 7, 21, 45, 69, 60, 21, 1, 1, 1, 8, 28, 71, 140, 181, 129, 34, 1, 1, 1, 9, 36, 105, 251, 431, 476, 277, 55, 1, 1, 1, 10, 45, 148, 413, 882, 1326, 1252, 595, 89, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Sums of antidiagonals are A099236. Main diagonal is A099237. Rows include A000045, A002478, A099234, A099235. Columns include A000217, A008778.

LINKS

Table of n, a(n) for n=0..77.

FORMULA

Square array T(n, k) = Sum_{j=0..n} binomial(k(n-j), j).

Rows are generated by 1/(1-x(1+x)^k) and satisfy a(n) = Sum_{k=0..n} binomial(n, k)a(n-k-1).

EXAMPLE

Rows begin

  1,   1,   1,   1,   1,   1, ...

  1,   1,   2,   3,   5,   8, ...

  1,   1,   3,   6,  13,  28, ...

  1,   1,   4,  10,  26,  69, ...

  1,   1,   5,  15,  45, 140, ...

Row 1 is the 0-section of 1/(1-x-x)   (A000079);

Row 2 is the 1-section of 1/(1-x-x^2) (A000045);

Row 3 is the 2-section of 1/(1-x-x^3) (A000930);

Row 4 is the 3-section of 1/(1-x-x^4) (A003269);

etc.

CROSSREFS

Cf. A099238.

Sequence in context: A047120 A096751 A293551 * A303912 A133815 A305027

Adjacent sequences:  A099230 A099231 A099232 * A099234 A099235 A099236

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)