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A217483 Alternating sums of the numbers in sequence A080253. 5
1, 2, 15, 132, 1565, 22918, 400939, 8160008, 189453369, 4942271754, 143128015943, 4556517918604, 158167223290453, 5945611873120910, 240619359452963427, 10430922482219093520, 482234053313600047217, 23683786738296923795986 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A365151 A140306 A143924 * A214043 A347993 A215922
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 04 2012
STATUS
approved

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Last modified February 21 16:55 EST 2024. Contains 370237 sequences. (Running on oeis4.)