A217488 Alternating sums of the squares of the numbers in sequence A080253.

1, 8, 281, 21328, 2858481, 596558808, 179058197641, 73110755339168, 38977936014004961, 26295624802015360168, 21898514473870334203641, 22064773395630274673891568, 26456951179676525013504937681, 37229662306608638451691410580088

Offset: 0

Author

Emanuele Munarini, Oct 04 2012

Keywords

• nonn

Crossrefs

Cf. A080253, A000670, A217483, A217484, A217485, A217486, A217487.

Programs

Mathematica

t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[Sum[(-1)^(n-k)c[k]^2, {k,0,n}], {n,0,100}]

Maxima

t(n):=sum(stirling2(n,k)*k!,k,0,n);
c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
makelist(sum((-1)^(n-k)*c(k)^2,k,0,n),n,0,40);

Formula

a(n) = sum((-1)^(n-k)*c(k)^2,k=0..n), where c(n) = A080253(n).

a(n) ~ (n!)^2 * 2^(2*n-1) / (log(2))^(2*n + 2). - Vaclav Kotesovec, Nov 27 2017