cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A336971 G.f. A(x) satisfies: A(x) = 1 - x^3 * A(x/(1 - x)) / (1 - x).

Original entry on oeis.org

1, 0, 0, -1, -1, -1, 0, 4, 15, 40, 86, 134, 16, -1060, -6119, -25187, -86678, -250846, -537819, -175233, 6998009, 55632942, 310923272, 1465146781, 6011047682, 20719304348, 49356093300, -36579100806, -1549214884054, -13807417413199, -92912464763743
Offset: 0

Views

Author

Ilya Gutkovskiy, Aug 09 2020

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 30; A[] = 0; Do[A[x] = 1 - x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 30}]

Formula

a(0) = 1, a(1) = a(2) = 0; a(n) = -Sum_{k=0..n-3} binomial(n-3,k) * a(k).

A346078 G.f. A(x) satisfies: A(x) = 1 + x - x^2 * A(x/(1 - x)) / (1 - x).

Original entry on oeis.org

1, 1, -1, -2, -2, 1, 11, 33, 61, 22, -418, -2363, -8375, -19715, -6325, 263490, 1950298, 9423505, 33042827, 59212141, -283826231, -3970508822, -28167479326, -148668438363, -571280079455, -848399025239, 11052089847863, 148600718966518, 1198795581209734
Offset: 0

Views

Author

Ilya Gutkovskiy, Jul 04 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 28; A[] = 0; Do[A[x] = 1 + x - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]

Formula

a(0) = a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).

A346079 G.f. A(x) satisfies: A(x) = x - x^2 * A(x/(1 - x)) / (1 - x).

Original entry on oeis.org

0, 1, 0, -1, -2, -2, 2, 17, 54, 109, 54, -796, -5000, -19499, -52252, -44617, 577554, 5071906, 27330978, 108557573, 263947354, -453137963, -11252508862, -92193933208, -545809325184, -2441788385255, -6271647457176, 22814756330975, 492197181810550, 4609129908957190
Offset: 0

Views

Author

Ilya Gutkovskiy, Jul 04 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 29; A[] = 0; Do[A[x] = x - x^2 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = 0; a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 29}]

Formula

a(0) = 0, a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).
Showing 1-3 of 3 results.