|
|
A119430
|
|
Expansion of Sum_{k>=0} 2^k*x^(2k)/Product_{j=1..k} (1 - j*2x).
|
|
2
|
|
|
1, 0, 2, 4, 12, 40, 152, 640, 2928, 14400, 75744, 424640, 2527552, 15902848, 105313408, 731376640, 5311088896, 40233525248, 317296341504, 2600091120640, 22099119279104, 194487001540608, 1769555559897088, 16622286300921856
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} S2(k,n-k)*2^k where S2(n,k)=A048993(n,k);
a(n) = Sum_{k=0..floor(n/2)} S2(n-k,k)*2^(n-k).
|
|
MATHEMATICA
|
a[n_] := Sum[2^(n-k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 09 2022 *)
|
|
PROG
|
(PARI) a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 08 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|