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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:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
B_{n + 1} = \sum_{k=0}^{n} {n \choose k} B_{k}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Sum∑nf(n)\sum_{n} f(n) Sum
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("1026e3"),
    Formula(Equal(BellNumber(Add(n, 1)), Sum(Mul(Binomial(n, k), BellNumber(k)), For(k, 0, n)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC