A119430 - OEIS

%I #18 Apr 09 2022 08:50:51

%S 1,0,2,4,12,40,152,640,2928,14400,75744,424640,2527552,15902848,

%T 105313408,731376640,5311088896,40233525248,317296341504,

%U 2600091120640,22099119279104,194487001540608,1769555559897088,16622286300921856

%N Expansion of Sum_{k>=0} 2^k*x^(2k)/Product_{j=1..k} (1 - j*2x).

%H Seiichi Manyama, <a href="/A119430/b119430.txt">Table of n, a(n) for n = 0..579</a>

%F a(n) = Sum_{k=0..n} S2(k,n-k)*2^k where S2(n,k)=A048993(n,k);

%F a(n) = Sum_{k=0..floor(n/2)} S2(n-k,k)*2^(n-k).

%t a[n_] := Sum[2^(n-k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* _Amiram Eldar_, Apr 09 2022 *)

%o (PARI) a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n-k, k, 2)); \\ _Seiichi Manyama_, Apr 08 2022

%Y Cf. A004211, A048993, A119429.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 19 2006