A217487 Partial sums of the squares of the numbers in sequence A080253.

1, 10, 299, 21908, 2901717, 602319006, 180257075455, 73470070612264, 39124516839956393, 26373727254869321522, 21951183825927218885331, 22108623093930072226980540, 26501124576166085360405809789, 37282620382364481062065321327558

Offset: 0

Author

Emanuele Munarini, Oct 04 2012

Keywords

• nonn

Crossrefs

Cf. A080253, A000670, A217483, A217484, A217485, A217486, A217488.

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[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(c(k)^2,k,0,n),n,0,40);

Formula

a(n) = sum(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