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A124311
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a(n) = Sum_{i=0..n} (-2)^i*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
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4
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1, -1, 5, -21, 121, -793, 5917, -49101, 447153, -4421105, 47062773, -535732805, 6484924585, -83079996041, 1121947980173, -15915567647101, 236442490569825, -3668776058118881, 59316847871113445, -997182232031471477, 17397298225094055897, -314449131128077197561
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OFFSET
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0,3
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COMMENTS
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The sequence has strictly alternating signs. The variant Dobinski-type formula e^(-1)* (2)^n * sum( (k-1/2)^n / k!,k=0..infinity) is strictly positive. - Karol A. Penson and Olivier Gerard, Oct 22 2007
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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E.g.f.: exp(exp(-2*x)-1+x). - Vladeta Jovovic, Aug 04 2007
G.f.: 1/U(0) where U(k)= 1 + x*(2*k+1) - 4*x^2*(k+1)/U(k+1) ; (continued fraction, 1-step). - Sergei N. Gladkovskii, Oct 11 2012
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MATHEMATICA
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Table[ Sum[ (-2)^(k) Binomial[n, k] BellB[k], {k, 0, n}], {n, 0, 50}] - Karol A. Penson and Olivier Gerard, Oct 22 2007
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PROG
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(Sage)
def A124311_list(n): # n>=1
T = [0]*(n+1); R = [1]
for m in (1..n-1):
a, b, c = 1, 0, 0
for k in range(m, -1, -1):
r = a + 2*(k*(b+c)+c)
if k < m : T[k+2] = u;
a, b, c = T[k-1], a, b
u = r
T[1] = u;
R.append((-1)^m*sum(T))
return R
A124311_list(22) # - Peter Luschny, Nov 02 2012
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CROSSREFS
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Cf. A000110, A000296, A005493, A126390, A126617.
Sequence in context: A015558 A168598 A002711 * A208593 A213009 A050910
Adjacent sequences: A124308 A124309 A124310 * A124312 A124313 A124314
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KEYWORD
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sign,changed
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AUTHOR
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N. J. A. Sloane, Aug 04 2007
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STATUS
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approved
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