A119430 Expansion of Sum_{k>=0} 2^k*x^(2k)/Product_{j=1..k} (1 - j*2x).

1, 0, 2, 4, 12, 40, 152, 640, 2928, 14400, 75744, 424640, 2527552, 15902848, 105313408, 731376640, 5311088896, 40233525248, 317296341504, 2600091120640, 22099119279104, 194487001540608, 1769555559897088, 16622286300921856

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..579

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

Cf. A004211, A048993, A119429.

Sequence in context: A204678 A025227 A211965 * A074034 A268952 A215072

Adjacent sequences: A119427 A119428 A119429 * A119431 A119432 A119433

Keyword

easy,nonn

Author

Paul Barry, May 19 2006

Status

approved