T07

Triangles
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$T_{07}(n,k)=\binom{n}{k}2^{n-k}(E_{n-k}(1/2)+E_{n-k}(1))$

Triangular form
1
1	0
-1	2	0
-2	-3	3	0
5	-8	-6	4	0
16	25	-20	-10	5	0
-61	96	75	-40	-15	6	0

sum	als	gcd	lcm
0	0	0	1
1	1	0	1
3	1	1	2
8	2	1	6
23	1	1	120
76	6	1	400
293	9	1	146400

Linear form (by rows)
Western	A173018	1,1,0,1,1,0,1,4
Eastern	A123125	1,0,1,0,1,1,0,1

Rectangular form
0	1	-1	-2	5	16	-61
0	2	-3	-8	25	96	-427
0	3	-6	-20	75	336	-1708
0	4	-10	-40	175	896	-5124
0	5	-15	-70	350	2016	-12810
0	6	-21	-112	630	4032	-28182
0	7	-28	-168	1050	7392	-56364

Fingerprint
Sub Seq	0	1	2	3
Row	A000111	A065619	A000000	A000000
Col	A000012	A000027	A000217	A007290
RowDiag	A000000	A000000	A000000	A000000
ColDiag	A000000	A000000	A000000	A000000
Characteristic	SUM	ALS	LCM	GCD
	A000667	A062162	A000000	A000000
	MIN	MAX	CENTRAL	MIDDLE
	A000007	A009006	A180056	A009006

Maple T07 := proc(n,k) binomial(n,k)*2^(n-k)*(euler(n-k,1/2)+euler(n-k,1)) end:

TeX T_{07}(n,k)=\binom{n}{k}2^{n-k}(E_{n-k}(1/2)+E_{n-k}(1))

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