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.

Previous Showing 21-25 of 25 results.

A213232 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^9)^3).

Original entry on oeis.org

1, 1, 4, 28, 215, 1983, 19789, 213698, 2426851, 28661509, 348287354, 4322627557, 54508747790, 695534616050, 8953637420349, 116002300640637, 1509724588732027, 19707310304585212, 257698683361191598, 3372154116182404890, 44121356408759264549
Offset: 0

Views

Author

Paul D. Hanna, Jun 06 2012

Keywords

Comments

Compare g.f. to:
(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 215*x^4 + 1983*x^5 + 19789*x^6 +...
Related expansions:
A(x)^9 = 1 + 9*x + 72*x^2 + 624*x^3 + 5661*x^4 + 54621*x^5 + 555837*x^6 +...
1/A(-x*A(x)^9)^3 = 1 + 3*x + 21*x^2 + 154*x^3 + 1446*x^4 + 14511*x^5 + 158838*x^6 +...

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, A213230, A213231, A213233.
Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
Cf. A213108, A213109, A213110, A213111, A213112, A213113.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^3, x, -x*subst(A^9, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

A213233 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^10)^4).

Original entry on oeis.org

1, 1, 5, 39, 345, 3512, 38431, 451620, 5587237, 72275004, 968509140, 13361356169, 188704259571, 2716467168169, 39716842554828, 588125693790055, 8800638181341593, 132838773216409675, 2019626662710709088, 30891440565153652705, 474899505740289874276
Offset: 0

Views

Author

Paul D. Hanna, Jun 06 2012

Keywords

Comments

Compare g.f. to:
(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).

Examples

			G.f.: A(x) = 1 + x + 5*x^2 + 39*x^3 + 345*x^4 + 3512*x^5 + 38431*x^6 +...
Related expansions:
A(x)^10 = 1 + 10*x + 95*x^2 + 960*x^3 + 10095*x^4 + 111212*x^5 +...
1/A(-x*A(x)^10)^4 = 1 + 4*x + 30*x^2 + 256*x^3 + 2605*x^4 + 28484*x^5 +...

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, A213230, A213231, A213232.
Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
Cf. A213108, A213109, A213110, A213111, A213112, A213113.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^4, x, -x*subst(A^10, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

A213227 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)).

Original entry on oeis.org

1, 1, 2, 8, 35, 181, 1042, 6301, 39435, 249744, 1585386, 10027385, 62696192, 385398251, 2322152120, 13727653882, 80274175978, 472701550856, 2883417403654, 18796497074750, 132728456810968, 995480740265410, 7605881152587204, 56821415293287735, 403362682583930224
Offset: 0

Views

Author

Paul D. Hanna, Jun 06 2012

Keywords

Comments

Compare g.f. to:
(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 35*x^4 + 181*x^5 + 1042*x^6 +...
Related expansions:
A(x)^6 = 1 + 6*x + 27*x^2 + 128*x^3 + 645*x^4 + 3462*x^5 + 19823*x^6 +...
1/A(-x*A(x)^6) = 1 + x + 5*x^2 + 20*x^3 + 108*x^4 + 638*x^5 + 3889*x^6 +...

Crossrefs

Cf. A213225, A213226, A213228, A213229, A213230, A213231, A213232, A213233.
Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
Cf. A213108, A213109, A213110, A213111, A213112, A213113.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A, x, -x*subst(A^6, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

A384894 G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^2.

Original entry on oeis.org

1, 1, 2, 1, -4, -14, -30, 12, 330, 1139, 2226, -2288, -39646, -163742, -410900, -89273, 5352720, 31177720, 114624554, 234094417, -312845870, -5584935715, -32878240028, -127407695297, -315375599410, 24759230680, 6177102106748, 44838273448641, 220383314338200
Offset: 0

Views

Author

Seiichi Manyama, Jun 12 2025

Keywords

Crossrefs

Column k=1 of A384899.
Cf. A000108, A213094, A213095, A384895.
Cf. A213091.

Programs

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

Formula

See A384899.

A385013 G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)^2).

Original entry on oeis.org

1, 1, 2, 4, 9, 19, 37, 52, -25, -630, -3616, -15897, -61476, -215135, -677464, -1823081, -3389900, 2523349, 73121734, 526205851, 2914005085, 14163375846, 62788424920, 255900158756, 945473736954, 3008738746058, 6827204137454, -2853842162077, -171206510083289
Offset: 0

Views

Author

Seiichi Manyama, Jun 15 2025

Keywords

Crossrefs

Column k=1 of A385017.
Cf. A000108, A213225, A213226, A384951.
Cf. A213091.

Programs

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

Formula

See A385017.
Previous Showing 21-25 of 25 results.

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