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 1-4 of 4 results.

A351756 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 2*x)) / (1 - 2*x)^2.

Original entry on oeis.org

1, 1, 5, 23, 119, 709, 4749, 35031, 281271, 2438565, 22673021, 224739303, 2363075191, 26246762213, 306830932749, 3763323446487, 48292462190743, 646763208308421, 9020009372203965, 130737162573013159, 1965798562640921879, 30613694640191725381
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 18 2022

Keywords

Crossrefs

Cf. A004211, A040027, A122704, A351757.

Programs

  • Mathematica
    nmax = 21; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 2 x)]/(1 - 2 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Formula

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

A351810 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 4*x)) / (1 - 4*x)^2.

Original entry on oeis.org

1, 1, 9, 69, 565, 5305, 56929, 680685, 8902349, 126121313, 1923133433, 31379181461, 544931376229, 10024917092105, 194602995875985, 3972686705253181, 85035210652191485, 1903471938128641457, 44453001710603619369, 1080789854059236415973, 27304602412815047204501
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A004213, A040027, A326324, A351756, A351757, A351811, A351812.

Programs

  • Mathematica
    nmax = 20; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 4 x)]/(1 - 4 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 4^(k-1) * a(n-k).

A351811 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.

Original entry on oeis.org

1, 1, 11, 101, 971, 10621, 133251, 1872261, 28840251, 481539021, 8658919571, 166768522101, 3421884596011, 74443313899901, 1710104876681571, 41338914172638021, 1048412294411955451, 27821558652073329261, 770663280948805164051, 22235353608667471453621
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A005011, A040027, A351756, A351757, A351810, A351812.

Programs

  • Mathematica
    nmax = 19; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 5 x)]/(1 - 5 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 5^(k-1) * a(n-k).

A351812 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 6*x)) / (1 - 6*x)^2.

Original entry on oeis.org

1, 1, 13, 139, 1531, 19021, 271453, 4358179, 76896931, 1471496341, 30333401893, 670125430219, 15784342627531, 394467249489661, 10415430504486733, 289527454704656659, 8447556960083354131, 258008113711846390981, 8228947382557338981973, 273472796359924298018299
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 19 2022

Keywords

Crossrefs

Cf. A005012, A040027, A351756, A351757, A351810, A351811.

Programs

  • Mathematica
    nmax = 19; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 6 x)]/(1 - 6 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 6^(k-1) * a(n-k).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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