A164976 Triangle read by rows, expansion of 1/(1-2*y*x-x+x^2-y*x^2).

1, 1, 2, 0, 5, 4, -1, 4, 16, 8, -1, -3, 25, 44, 16, 0, -10, 7, 102, 112, 32, 1, -8, -41, 97, 344, 272, 64, 1, 4, -74, -80, 528, 1040, 640, 128, 0, 15, -33, -366, 121, 2168, 2928, 1472, 256, -1, 12, 75, -426, -1219, 1898, 7664, 7840, 3328, 512

Offset

0,3

Comments

Leftmost column is A010892.

Rows sum up to A000244 and diagonals to A000073.

A164975 has a similar g.f.: x/(1-2*y*x-x-x^2+y*x^2).. - Georg Fischer, Oct 15 2023

Links

Georg Fischer, Table of n, a(n) for n = 1..5050

Example

Triangle begins:
   1;
   1,   2;
   0,   5,   4;
  -1,   4,  16,   8;
  -1,  -3,  25,  44,  16;
   0, -10,   7, 102, 112,  32;
   1,  -8, -41,  97, 344, 272, 64;
  ...

Maple

s := 1/(1-2*y*x-x+x^2-y*x^2): t := series(s, x, 12):
seq(print(seq(coeff(coeff(t, x, n), y, m), m=0..n)), n=0..11); # Georg Fischer, Oct 15 2023

Crossrefs

Cf. A164975, A000244, A000045, A164965, A000073.

Cf. A010892 (1st column), A000079 (right diagonal).

Sequence in context: A173732 A086280 A349950 * A261745 A083714 A215481

Adjacent sequences: A164973 A164974 A164975 * A164977 A164978 A164979

Keyword

tabl,sign

Author

Mark Dols, Sep 03 2009

Extensions

Missing commas inserted in what used to be the term "1-8-41" (now "1,-8,-41") by Geoff Bailey (geoff(AT)maths.usyd.edu.au), Nov 30 2009

Definition changed by Georg Fischer, Oct 15 2023

Status

approved