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A117435 Triangle related to exp(x)cos(2x). 2
1, 0, 1, -4, 0, 1, 0, -12, 0, 1, 16, 0, -24, 0, 1, 0, 80, 0, -40, 0, 1, -64, 0, 240, 0, -60, 0, 1, 0, -448, 0, 560, 0, -84, 0, 1, 256, 0, -1792, 0, 1120, 0, -112, 0, 1, 0, 2304, 0, -5376, 0, 2016, 0, -144, 0, 1, -1024, 0, 11520, 0, -13440, 0, 3360, 0, -180, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A006495 (with e.g.f. exp(x)cos(2x)). Inverse is A117436. Diagonal sums are (1,0,-3,0,5,0,-7,...). Diagonals correspond to rows of A117438.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Number triangle whose k-th column has e.g.f. (x^k/k!)*cos(2x); T(n,k)=C(n,k)*(-4)^((n-k)/2)*(1+(-1)^(n-k))/2.

EXAMPLE

Triangle begins

1,

0, 1,

-4, 0, 1,

0, -12, 0, 1,

16, 0, -24, 0, 1,

0, 80, 0, -40, 0, 1,

-64, 0, 240, 0, -60, 0, 1

CROSSREFS

Cf. A117411.

Sequence in context: A046781 A244530 A271424 * A282252 A268367 A117436

Adjacent sequences:  A117432 A117433 A117434 * A117436 A117437 A117438

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Mar 16 2006

STATUS

approved

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Last modified August 23 13:42 EDT 2017. Contains 291004 sequences.