A217483 Alternating sums of the numbers in sequence A080253.

1, 2, 15, 132, 1565, 22918, 400939, 8160008, 189453369, 4942271754, 143128015943, 4556517918604, 158167223290453, 5945611873120910, 240619359452963427, 10430922482219093520, 482234053313600047217, 23683786738296923795986

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = sum((-1)^(n-k)*c(k),k=0..n), where c(n) = A080253(n).

E.g.f.: exp(x)/(2-exp(2*x)) - (1/2)*exp(-x)*log(1/(2-exp(2*x))). - corrected by Vaclav Kotesovec, Nov 27 2017

a(n) ~ n! * 2^(n - 1/2) / (log(2))^(n+1). - 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], {k, 0, n}], {n, 0, 100}]
nmax = 20; CoefficientList[Series[E^x/(2 - E^(2*x)) + Log[2 - E^(2*x)] / (2*E^x), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 27 2017 *)

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), k, 0, n), n, 0, 10);

Crossrefs

Cf. A080253, A000670, A217484, A217485, A217486, A217487, A217488.

Sequence in context: A140306 A374975 A143924 * A371579 A214043 A347993

Adjacent sequences: A217480 A217481 A217482 * A217484 A217485 A217486

Keyword

nonn

Author

Emanuele Munarini, Oct 04 2012

Status

approved