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COMMENT
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this sequence generates the fifth terms of the following sequences:
a(2)=52=A000110(5), a(3)=43833=A020556(5), a(4)=149670844=A069223(5),
a(5)=1346634725665=A071379(5),a(6)=25571928251231076=A070227(5)
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FORMULA
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Sequence defined through the following hypergeometric-type generating function, in Maple notation:
exp(-1)*sum(hypergeom([k+1,k+1,k+1,k+1],[1,1,1,1],x)/k!,k=0..infinity)=sum(a(n)*x^n/(n!)^5,n=0..infinity),
which is itself an infinite sum of hypergeometric functions.
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