basis_map / A130595
Image under a basis map u^k -> P_k. All operations
Parameters (34)
- all
- A007318 223 proof steps, 219 sequences
- A008277 214 proof steps, 212 sequences
- A013609 212 proof steps, 210 sequences
- A013610 212 proof steps, 210 sequences
- A013611 212 proof steps, 210 sequences
- A008288 28 proof steps, 13 sequences
- A027465 7 proof steps, 7 sequences
- A027466 7 proof steps, 7 sequences
- A027467 7 proof steps, 7 sequences
- A038255 6 proof steps, 6 sequences
- A038279 6 proof steps, 6 sequences
- A038291 6 proof steps, 6 sequences
- A038303 6 proof steps, 6 sequences
- A038327 6 proof steps, 6 sequences
- A038207 6 proof steps, 6 sequences
- A038231 6 proof steps, 6 sequences
- A038243 6 proof steps, 6 sequences
- A130595 3 proof steps, 3 sequences
- A049020 2 proof steps, 2 sequences
- A154602 1 proof steps, 1 sequences
- A159834 1 proof steps, 1 sequences
- A341287 1 proof steps, 1 sequences
- A056242 1 proof steps, 1 sequences
- A060821 1 proof steps, 1 sequences
- A063967 1 proof steps, 1 sequences
- A026729 1 proof steps, 1 sequences
- A066325 1 proof steps, 1 sequences
- A099040 1 proof steps, 1 sequences
- A099093 1 proof steps, 1 sequences
- A099097 1 proof steps, 1 sequences
- A030528 1 proof steps, 1 sequences
- A111125 1 proof steps, 1 sequences
- A112227 1 proof steps, 1 sequences
- A113953 1 proof steps, 1 sequences
3 sequences
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A130595: Triangle read by rows: lower triangular matrix which is inverse to Pascal's triangle (A007318) regarded as a lower triangular matrix.
basis-map coefficients of A026729 → basis A1305951 · -1, 1 · 1, -2, 1 · -1, 3, -3, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
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A021012: Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).
basis-map coefficients of A021012 → basis A1305951 · 1, -1 · 2, -4, 2 · 6, -18, 18, -6 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
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A094645: Triangle of generalized Stirling numbers of the first kind read by rows: T(n, k) = (-1)^(n+k)*Sum_{m=0..n} Stirling1(n, m) * binomial(m, k), where Stirling1 is A048994.
A028338 → x ↦ 2x−31 · -1, 1 · 0, -1, 1 · 0, -1, 0, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …