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 11-17 of 17 results.

A213230 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^2).

Original entry on oeis.org

1, 1, 3, 18, 115, 902, 7722, 70784, 678251, 6670586, 66851992, 677328214, 6903177354, 70490174298, 718856047396, 7304677030708, 73837797474235, 741722190452840, 7402780597473820, 73459355234486763, 726095774886910232, 7170907377415662763, 71063833561266044578
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 + 3*x^2 + 18*x^3 + 115*x^4 + 902*x^5 + 7722*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 52*x^2 + 368*x^3 + 2754*x^4 + 22112*x^5 + 189344*x^6 +...
1/A(-x*A(x)^8)^2 = 1 + 2*x + 13*x^2 + 78*x^3 + 634*x^4 + 5488*x^5 + 50969*x^6 +...

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, 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^2, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

A213231 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^3).

Original entry on oeis.org

1, 1, 4, 25, 176, 1431, 12526, 117850, 1167446, 12080563, 129326575, 1422908670, 15999766613, 183070661566, 2124252427416, 24929036429880, 295250330398281, 3523043486823439, 42294807342916249, 510274778010082846, 6181011777164665559, 75112032752942278141
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 + 25*x^3 + 176*x^4 + 1431*x^5 + 12526*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 60*x^2 + 480*x^3 + 3998*x^4 + 34968*x^5 + 318888*x^6 +...
1/A(-x*A(x)^8)^3 = 1 + 3*x + 18*x^2 + 121*x^3 + 987*x^4 + 8646*x^5 + 82244*x^6 +...

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, A213230, 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^3, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

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), ", "))

A384857 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^3 ).

Original entry on oeis.org

1, 1, 7, 46, 361, -6284, -632951, -31583474, -1484748191, -51928436312, -303653774159, 219248741052826, 35743757192135425, 4097960104621191004, 408462300514973323753, 33384541884258873033406, 1521231207001104466842049, -200132739000502301652035888, -84772475888572203988197350303
Offset: 0

Views

Author

Seiichi Manyama, Jun 10 2025

Keywords

Crossrefs

Column k=1 of A384861.
Cf. A052752, A213112, A213113, A384855, A384856, A384858.
Cf. A213109.

Programs

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

Formula

See A384861.

A384803 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^4) ).

Original entry on oeis.org

1, 1, 3, 28, 365, 7456, 198967, 6600448, 260641817, 11805179392, 603174969611, 34119591645184, 2107808150141509, 140656454965522432, 10045467848093258687, 762717885873201995776, 61259933997939643876913, 5188866020593647457533952, 463236056771875012276202899
Offset: 0

Views

Author

Seiichi Manyama, Jun 10 2025

Keywords

Crossrefs

Column k=1 of A384804.
Cf. A213108, A213109.

Programs

  • PARI
    a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-4*n+4*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));

Formula

See A384804.
Previous Showing 11-17 of 17 results.

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