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.

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).

A379279 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^2) * (1 + x*A(x)) )^2.

Original entry on oeis.org

1, 4, 30, 288, 3125, 36490, 447478, 5683186, 74105002, 986302778, 13344661479, 182998935930, 2537838036761, 35530970858236, 501523116910044, 7129275916213606, 101973703002773268, 1466574750062589956, 21194869324964207133, 307642575576365729486, 4482940969372057898247
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(2*n+2*k+2, 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 A215715.
a(n) = Sum_{k=0..n} binomial(2*n+2*k+2,k) * binomial(2*n+2*k+2,n-k)/(n+k+1).

A379281 G.f. A(x) satisfies A(x) = 1/( (1 - x) * (1 - x*A(x)) )^2.

Original entry on oeis.org

1, 4, 18, 96, 575, 3706, 25078, 175666, 1262723, 9261018, 69024147, 521281642, 3980391050, 30678331440, 238350850248, 1864751821958, 14678131286357, 116160233811868, 923684828888152, 7376541052964806, 59137050311947284, 475757909357776656, 3839678158239147611
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Programs

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

Formula

G.f.: B(x)^2 where B(x) is the g.f. of A199475.
a(n) = 2 * Sum_{k=0..n} binomial(2*n-k+2,k) * binomial(3*n-3*k+1,n-k)/(2*n-k+2).
Showing 1-3 of 3 results.