# Compositions into parts with even multiplicities

Wed Aug 8 11:44:09 CEST 2007

```Seqfans,

Below is my submission of a new sequence:

Number of compositions of 2n in which each part has even multiplicity.

Is there an "elegant" formula/GF for this seq.?

Regards,
V.

%I A000001
%S A000001 1,2,8,24,72,264,952,3352,11960,43656,160840,594568,2215480,8300056,31191480,117674504,445439944,1691011464,6437425720,24564925848,93937631544,359943235080
%N A000001 Number of compositions of 2n in which each part has even multiplicity.
%e A000001 Table of n, a(n) for n = 1..50

1 1
2 2
3 8
4 24
5 72
6 264
7 952
8 3352
9 11960
10 43656
11 160840
12 594568
13 2215480
14 8300056
15 31191480
16 117674504
17 445439944
18 1691011464
19 6437425720
20 24564925848
21 93937631544
22 359943235080
23 1381706541512
24 5312678458888
25 20458827990456
26 78898261863832
27 304666752525368
28 1177917296854152
29 4559335129446984
30 17666556675108360
31 68523021533870264
32 266028985353139480
33 1033724645977633464
34 4020146511369758088
35 15646589432891059528
36 60942410793471545736
37 237533290605090589752
38 926442358309657850904
39 3615653152390623771320
40 14119392491623156786440
41 55168805915171545165000
42 215678977387306093805960
43 843621907465521599000120
44 3301441176541292976425112
45 12926040490322737955361336
46 50631974207069619560250632
47 198414469648363719485005768
48 777863140397512864870792200
49 3050753611395618694067041976
50 11969563573001226379198699672
%O A000001 1
%K A000001 ,nonn,