Real-rooted atlas
Polynomial sequences with integer coefficients whose roots are all real, proved for every row. Each sequence comes with its recurrence, its proof, and its OEIS matches.
3,043 sequences · 1,922 OEIS entries
Search by a row of coefficients, row sums, an OEIS number or a name. Try 1, 4, 1, A008292 or narayana.
Examples
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Eulerian numbers
A008292
1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 …
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Narayana numbers
A001263
1 · 1, 1 · 1, 3, 1 · 1, 6, 6, 1 …
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A decomposition of the double factorials
A156919
A185410 → reverse1 · 0, 1 · 0, 2, 1 · 0, 4, 10, 1 …
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From the Delannoy triangle
A209695
delannoy → x ↦ x/(x+1)1 · 1, 2 · 1, 5, 5 · 1, 8, 18, 12 …
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A θ-image of the binomial triangle
A125092
A007318 → (θ+1)²1 · 1, 4 · 1, 8, 9 · 1, 12, 27, 16 …
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γ-vectors of the Eulerian polynomials
A101280
A008292 → γ (shift +1)1 · 1 · 1, 2 · 1, 8 …