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

0,2

Links

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

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

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}]

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(c(k), k, 0, n), n, 0, 10);

Crossrefs

Cf. A080253, A000670, A217483, A217485, A217486, A217487, A217488.

Sequence in context: A339233 A107872 A008858 * A078670 A317104 A163948

Adjacent sequences: A217481 A217482 A217483 * A217485 A217486 A217487

Keyword

nonn

Author

Emanuele Munarini, Oct 04 2012

Status

approved