A217484 Partial sums of the numbers in sequence A080253.

1, 4, 21, 168, 1865, 26348, 450205, 9011152, 206624529, 5338349652, 153408637349, 4853054571896, 167576795780953, 6271355892192316, 252836327218276653, 10924378168890333600, 503589353964709474337, 24669610145575233317540

Offset: 0

Author

Emanuele Munarini, Oct 04 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A080253, A000670, A217483, A217485, A217486, A217487, 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], {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),k,0,n),n,0,10);

Formula

a(n) = sum(c(k),k=0..n), where c(n) = A080253(n).

E.g.f.: exp (x)/(2-exp(2*x)) + x*exp (x)/2 + (1/4)*exp(x)*log(1/(2-exp(2*x))). - corrected by Vaclav Kotesovec, Jan 02 2013

a(n) ~ n! * 2^(n-1/2)/(log(2))^(n+1). - Vaclav Kotesovec, Jan 02 2013