A097341 a(n) = Sum_{k=0..floor(n/2)} Stirling2(n-k,k) * 2^k.

1, 0, 2, 2, 6, 14, 38, 110, 342, 1134, 3990, 14830, 58006, 237998, 1021462, 4574318, 21325462, 103287598, 518768406, 2697426926, 14498316182, 80440333998, 460112203798, 2710038058862, 16418576767126, 102212840258094, 653247225514262, 4282249051881198

Offset: 0

Author

Paul Barry, Aug 05 2004

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..654

Crossrefs

Cf. A024427, A097342, A119429, A119430, A171367.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, 2^k*x^(2*k)/prod(j=1, k, 1-j*x))) \\ Seiichi Manyama, Apr 09 2022

PARI

a(n) = sum(k=0, n\2, 2^k*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 09 2022

Formula

a(n)=sum{k=0..floor(n/2), sum{i=0..k, (-1)^(k+i)i^(n-k)/(i!(k-i)!)}2^k }

G.f.: Sum_{k>=0} 2^k * x^(2*k)/Product_{j=1..k} (1 - j * x). - Seiichi Manyama, Apr 09 2022