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.

A367236 G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^2)^2.

Original entry on oeis.org

1, 1, 2, 7, 26, 107, 462, 2074, 9572, 45147, 216638, 1054254, 5190710, 25810064, 129423512, 653740518, 3323270096, 16988894131, 87283137130, 450434292624, 2333851816654, 12136369892776, 63318984098996, 331347363084737, 1738713937163124, 9146850725274636
Offset: 0

Views

Author

Seiichi Manyama, Nov 11 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=2, t=0, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));

Formula

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

A367238 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^2)^2.

Original entry on oeis.org

1, 1, 5, 31, 219, 1672, 13439, 112043, 960017, 8402085, 74791408, 675033956, 6163120105, 56820187321, 528231686315, 4946304326883, 46609889424547, 441664236745594, 4205848369345681, 40228631544942031, 386317524696654392, 3723196299965400616
Offset: 0

Views

Author

Seiichi Manyama, Nov 11 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=2, t=3, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));

Formula

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

A367282 G.f. satisfies A(x) = 1 + x*A(x)^2 * (1 + x*A(x)^2)^2.

Original entry on oeis.org

1, 1, 4, 18, 94, 527, 3108, 18993, 119214, 763997, 4978304, 32883853, 219690066, 1481858835, 10078051830, 69030877581, 475795428158, 3297527987794, 22965847261928, 160649189379029, 1128201207643744, 7951399289858530, 56222323349767666
Offset: 0

Views

Author

Seiichi Manyama, Nov 12 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n, s=2, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));

Formula

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