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.

A379251 G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^2) )^2.

Original entry on oeis.org

1, 4, 32, 340, 4144, 54724, 761712, 11004500, 163453472, 2480507524, 38292849280, 599455647828, 9493724671184, 151835354054212, 2448792546337360, 39781755539153748, 650386418008379200, 10692713526634029316, 176669496568313495520, 2931998993134971532116, 48854054306918652620912
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A361638.
a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(2*n+2*k+2,n-k)/(n+k+1).

A379280 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3) * (1 + x*A(x)) )^2.

Original entry on oeis.org

1, 4, 38, 500, 7601, 125520, 2187736, 39608616, 737651032, 14040612502, 271931510448, 5341639974490, 106167131932708, 2131125360950758, 43142742495766252, 879810600033569754, 18057207334571432048, 372701480245014988624, 7731178967720860156743
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A364333.
a(n) = Sum_{k=0..n} binomial(2*n+4*k+2,k) * binomial(2*n+4*k+2,n-k)/(n+2*k+1).

A379283 G.f. A(x) satisfies A(x) = 1/( (1 - x*A(x)^3) * (1 - x*A(x)) )^2.

Original entry on oeis.org

1, 4, 42, 612, 10387, 192312, 3766316, 76716624, 1608691229, 34495221722, 752911467734, 16671973428486, 373609441084507, 8457057155407906, 193087102810266948, 4441320670474030222, 102821800799622552713, 2394063264658388861914, 56025225620739219372819
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A379287.
a(n) = 2 * Sum_{k=0..n} binomial(2*n+5*k+2,k) * binomial(3*n+3*k+1,n-k)/(2*n+5*k+2).
Showing 1-3 of 3 results.