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.

A365110 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^3.

Original entry on oeis.org

1, 1, -3, 3, 11, -54, 66, 297, -1575, 1980, 10300, -55392, 68352, 403583, -2153685, 2551845, 16999045, -89142087, 99986901, 750955382, -3850437018, 4041467331, 34310059311, -171533033904, 166630375248, 1607168518073, -7821913867611, 6950050797297
Offset: 0

Views

Author

Seiichi Manyama, Aug 22 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=3) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

A365111 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^4.

Original entry on oeis.org

1, 1, -4, 6, 16, -119, 240, 630, -5656, 13044, 31568, -323102, 816172, 1772553, -20373748, 55339784, 105991968, -1366239119, 3950894080, 6570520544, -95534073488, 292319792622, 414994066768, -6884779019086, 22198354364212, 26341578132594, -507524582140912
Offset: 0

Views

Author

Seiichi Manyama, Aug 22 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=4) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

A365112 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^5.

Original entry on oeis.org

1, 1, -5, 10, 20, -220, 624, 940, -15220, 52090, 49310, -1254070, 4951430, 2039640, -113088840, 505430700, -42379684, -10748423405, 53899438385, -29300595085, -1054751754795, 5914944193114, -5760460624890, -105478270711140, 661900612108440, -914408777470140
Offset: 0

Views

Author

Seiichi Manyama, Aug 22 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=5) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
Showing 1-3 of 3 results.