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.

A351437 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^2.

Original entry on oeis.org

1, 1, 1, 3, 7, 17, 47, 145, 481, 1691, 6295, 24805, 103095, 449805, 2052081, 9762699, 48334855, 248568321, 1325297879, 7312927481, 41694974649, 245288605059, 1487041552343, 9279329735685, 59537092965663, 392371097100373, 2653606218921673, 18400405626141667, 130712743774279015
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 11 2022

Keywords

Crossrefs

Programs

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

A351283 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.

Original entry on oeis.org

1, 1, 1, 5, 16, 46, 142, 496, 1888, 7538, 31291, 135739, 617461, 2939215, 14575027, 75014471, 399901294, 2205630124, 12572140372, 73961880118, 448447331338, 2798640572516, 17956583819425, 118336081817953, 800278211629795, 5549154792085813, 39420390891260821
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 12 2022

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 26; A[] = 0; Do[A[x] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, k + 3] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]

Formula

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

A351648 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^5.

Original entry on oeis.org

1, 1, 1, 6, 22, 69, 224, 819, 3296, 13942, 60941, 276399, 1309207, 6479609, 33377271, 178186018, 983386188, 5604262733, 32955823822, 199771724691, 1246747659198, 8000380516898, 52728354046939, 356593588048023, 2472544614851517, 17563971319301049, 127727505109579581
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 16 2022

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 26; A[] = 0; Do[A[x] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^5 + 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 + 4] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]

Formula

a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n+2,k+4) * a(k).
Showing 1-3 of 3 results.