|
%I #15 Jun 06 2013 17:07:16
%S 1,4,21,168,1865,26348,450205,9011152,206624529,5338349652,
%T 153408637349,4853054571896,167576795780953,6271355892192316,
%U 252836327218276653,10924378168890333600,503589353964709474337,24669610145575233317540
%N Partial sums of the numbers in sequence A080253.
%H Vincenzo Librandi, <a href="/A217484/b217484.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = sum(c(k),k=0..n), where c(n) = A080253(n).
%F 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
%F a(n) ~ n! * 2^(n-1/2)/(log(2))^(n+1). - _Vaclav Kotesovec_, Jan 02 2013
%t 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}]
%o (Maxima) t(n):=sum(stirling2(n,k)*k!,k,0,n);
%o c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
%o makelist(sum(c(k),k,0,n),n,0,10);
%Y Cf. A080253, A000670, A217483, A217485, A217486, A217487, A217488.
%K nonn
%O 0,2
%A _Emanuele Munarini_, Oct 04 2012
|
