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A052844
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E.g.f.: exp(x*(2-x)/(1-x)).
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3
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1, 2, 6, 26, 148, 1032, 8464, 79592, 842832, 9914336, 128162464, 1804852128, 27489582784, 450089665664, 7880963503872, 146913179393408, 2904309329449216, 60677563647195648, 1335634021282590208, 30891084696208976384, 748854186528315687936
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OFFSET
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0,2
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COMMENTS
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An unspecified number of sign-in sheets are available at a meeting of n people. The attendees sign in on one of the sheets in the order that they arrive at the meeting. But some, none, or all of the attendees forget to sign in. a(n) is the number of ways this can happen.
Previous name was: A simple grammar.
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LINKS
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FORMULA
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E.g.f.: exp(x*(-2+x)/(-1+x)).
Recurrence: {a(0)=1, a(1)=2, a(2)=6, (-2-n^2-3*n)*a(n)+(n^2+5*n+6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)}.
a(n) = n!*sum(m=1,n, ((sum(j=0,m, binomial(m,j)*binomial(n-j-1,m-j-1))))/m!)+1; [Vladimir Kruchinin, May 02 2012]
E.g.f. = exp(x)*exp(x/(1-x)) so a(n) = Sum_{k = 0..n} binomial(n,k)*A000262(k). - Peter Bala May 14 2012
a(0) = 1; a(n) = a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * k! * a(n-k). - Ilya Gutkovskiy, Aug 13 2021
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MAPLE
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spec := [S, {B=Sequence(Z, 1 <= card), C=Union(Z, B), S=Set(C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[Exp[x/(1 - x)] Exp[x], {x, 0, 20}], x]*
Table[n!, {n, 0, 20}]
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PROG
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(Maxima) a(n):=n!*sum(((sum(binomial(m, j)*binomial(n-j-1, m-j-1), j, 0, m)))/m!, m, 1, n)+1; \\ Vladimir Kruchinin, May 02 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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