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

0,2

Links

Table of n, a(n) for n=0..13.

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

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}]

Prog

(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);

Crossrefs

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

Sequence in context: A079929 A226415 A226346 * A332128 A247484 A136364

Adjacent sequences: A217485 A217486 A217487 * A217489 A217490 A217491

Keyword

nonn

Author

Emanuele Munarini, Oct 04 2012

Status

approved