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Fungrim entry: 1026e3

Bn+1=k=0n(nk)BkB_{n + 1} = \sum_{k=0}^{n} {n \choose k} B_{k}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
B_{n + 1} = \sum_{k=0}^{n} {n \choose k} B_{k}

n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Sumnf(n)\sum_{n} f(n) Sum
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(BellNumber(Add(n, 1)), Sum(Mul(Binomial(n, k), BellNumber(k)), For(k, 0, n)))),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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2021-03-15 19:12:00.328586 UTC