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 1-2 of 2 results.

A371693 G.f. satisfies A(x) = ( 1 + x * A(x) * (1 + A(x)) )^2.

Original entry on oeis.org

1, 4, 28, 248, 2480, 26688, 301648, 3531424, 42449088, 520858496, 6497190528, 82146802944, 1050370074624, 13559126110720, 176469550681344, 2313050095245824, 30506619439926272, 404558181197010944, 5391161355764205568, 72156618656648237056, 969557980700415827968
Offset: 0

Views

Author

Seiichi Manyama, Apr 03 2024

Keywords

Crossrefs

Column k=2 of A378239.
Cf. A219534.

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A219534.
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2*n+2*k+2,n)/(n+k+1).

A371989 G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)*(1 + A(x)) )^(1/3).

Original entry on oeis.org

1, 6, 18, -18, -270, 486, 7938, -17010, -290142, 676998, 11852082, -29091474, -518183406, 1315388646, 23720180130, -61672468338, -1122411776958, 2971089997830, 54459919690578, -146181889695762, -2694816626063310, 7314502270743270, 135469313469987138
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 9^n*sum(k=0, n, binomial(n, k)*binomial(n/3+k/3+1/3, n)/(n+k+1));

Formula

a(n) = 9^n * Sum_{k=0..n} binomial(n,k) * binomial(n/3+k/3+1/3,n)/(n+k+1).
Showing 1-2 of 2 results.