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.

A364645 G.f. satisfies A(x) = 1/(1 - 3*x) - x*A(x)^3.

Original entry on oeis.org

1, 2, 3, 6, 19, 51, 114, 312, 981, 2616, 6564, 19647, 59922, 159056, 430302, 1329996, 3926217, 10498968, 30052851, 93244764, 267690168, 729649143, 2173840338, 6663260223, 18768583674, 52570016676, 160362713250, 481809941520, 1346473504182, 3886164785178
Offset: 0

Views

Author

Seiichi Manyama, Jul 31 2023

Keywords

Links

Crossrefs

Cf. A364641, A364646, A364647.
Cf. A005773, A349254, A349256, A349534.

Programs

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

Formula

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

A364646 G.f. satisfies A(x) = 1/(1 - 4*x) - x*A(x)^3.

Original entry on oeis.org

1, 3, 7, 16, 55, 235, 856, 2664, 9055, 37417, 151431, 533452, 1825972, 7141860, 29778280, 113688592, 400940751, 1499506693, 6185139781, 24862774872, 91529003839, 334939413067, 1338383383444, 5510330536000, 21217042841668, 77850045234108, 300471644949940
Offset: 0

Views

Author

Seiichi Manyama, Jul 31 2023

Keywords

Crossrefs

Cf. A364641, A364645, A364647.
Cf. A001700, A349535.

Programs

  • PARI
    a(n) = sum(k=0, n, (-1)^k*4^(n-k)*binomial(n+k, 2*k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^k * 4^(n-k) * binomial(n+k,2*k) * binomial(3*k,k) / (2*k+1).

A364647 G.f. satisfies A(x) = 1/(1 - 5*x) - x*A(x)^3.

Original entry on oeis.org

1, 4, 13, 38, 135, 677, 3538, 15868, 63313, 268430, 1348190, 7038185, 33328258, 144159428, 642323050, 3213846836, 16700677289, 80935833050, 363843867265, 1660048399600, 8276473557820, 42830085070355, 210286731046320, 967456811687945, 4476690297795850
Offset: 0

Views

Author

Seiichi Manyama, Jul 31 2023

Keywords

Crossrefs

Cf. A364641, A364645, A364646.
Cf. A026378.

Programs

  • PARI
    a(n) = sum(k=0, n, (-1)^k*5^(n-k)*binomial(n+k, 2*k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * binomial(n+k,2*k) * binomial(3*k,k) / (2*k+1).
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.