A236967 Expansion of (1+3*x)^2/(1-3*x)^2.

1, 12, 72, 324, 1296, 4860, 17496, 61236, 209952, 708588, 2361960, 7794468, 25509168, 82904796, 267846264, 860934420, 2754990144, 8781531084, 27894275208, 88331871492, 278942752080, 878669669052, 2761533245592, 8661172452084, 27113235502176, 84728860944300

Offset: 0

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Apr 22 2014

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-9)

Crossrefs

Cf. Expansion of (1 + k*x)^m/(1 - k*x)^m where the values of k,m are:

......|..m = 1..|..m = 2..|..m = 3..|..m = 4..|..m = 5..|..m = 6..|

k = 1 | A040000 | A008574 | A005899 | A008412 | A008413 | A008414 |

k = 2 | A151821 | A241204 | | | | |

k = 3 | A099856 | A236967 | | | | |

k = 4 | A081654 | | | | | |

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Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x)^2/(1-3*x)^2));

Formula

For n >= 1, a(n) = 4*n*3^n. - Robert Israel, May 08 2014

Extensions

Edited by Wolfdieter Lang, May 07 2014