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 1-10 of 17 results. Next

A124531 Row 1 of rectangular table A124530.

Original entry on oeis.org

1, 1, 2, 5, 16, 62, 274, 1332, 6978, 38873, 228090, 1399625, 8933506, 59066261, 403241292, 2835267821, 20490128048, 151951503074, 1154770194362, 8983396031267, 71473650532630, 581142591346325, 4825842125683150
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124532, A124533, A124534, A124535, A124536.

Programs

  • PARI
    a(n)=local(R);R=vector(n+2,r,vector(n+2,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[2][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^n, where R_n(x) is the g.f. of row n in table A124530.

A124535 Row 5 of rectangular table A124530.

Original entry on oeis.org

1, 1, 6, 36, 216, 961, 5977, 39363, 271564, 1949165, 14487241, 111115804, 877086405, 7109569724, 59075905996, 502464618671, 4369068613929, 38796820526316, 351496911119002, 3246426019892427, 30543990287835441
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124533, A124534, A124536.

Programs

  • PARI
    a(n)=local(R);R=vector(n+6,r,vector(n+6,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[6][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(5n), where R_n(x) is the g.f. of row n in table A124530.

A124532 Row 2 of rectangular table A124530.

Original entry on oeis.org

1, 1, 3, 10, 39, 174, 858, 4564, 25793, 153301, 951325, 6130757, 40861658, 280767621, 1983859580, 14385651988, 106878699675, 812480791324, 6312686006725, 50083418434737, 405430892640225, 3346568909331984
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124533, A124534, A124535, A124536.

Programs

  • PARI
    a(n)=local(R);R=vector(n+3,r,vector(n+3,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[3][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(2n), where R_n(x) is the g.f. of row n in table A124530.

A124533 Row 3 of rectangular table A124530.

Original entry on oeis.org

1, 1, 4, 16, 71, 351, 1891, 10888, 66139, 420235, 2775981, 18978873, 133828922, 970678790, 7226115267, 55115404005, 430080085093, 3429311454089, 27912555377062, 231710034354364, 1960247357996533, 16889105788701591
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124534, A124535, A124536.

Programs

  • PARI
    a(n)=local(R);R=vector(n+4,r,vector(n+4,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[4][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(3n), where R_n(x) is the g.f. of row n in table A124530.

A124534 Row 4 of rectangular table A124530.

Original entry on oeis.org

1, 1, 5, 25, 113, 608, 3535, 21844, 141809, 959882, 6738850, 48877221, 365145267, 2803002587, 22066904802, 177881536038, 1466278969213, 12345543329079, 106069531868783, 929158597546721, 8292429187449462, 75348425058995464
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124533, A124535, A124536.

Programs

  • PARI
    a(n)=local(R);R=vector(n+5,r,vector(n+5,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[5][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(4n), where R_n(x) is the g.f. of row n in table A124530.

A124536 Row 6 of rectangular table A124530.

Original entry on oeis.org

1, 1, 7, 49, 343, 2401, 9430, 65810, 480077, 3637345, 28502254, 230271472, 1913354190, 16318251874, 142611810220, 1275372111383, 11657396456231, 108792892306605, 1035708759921763, 10049835806235885, 99321845447658052
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Crossrefs

Cf. A124530 (table); other rows: A124531, A124532, A124533, A124534, A124535.

Programs

  • PARI
    a(n)=local(R);R=vector(n+7,r,vector(n+7,c,if(r==1 || c<=2,1,r^(c-2)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[7][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(6n), where R_n(x) is the g.f. of row n in table A124530.

A124542 Row 2 of rectangular table A124540; equals the self-convolution of A124532 (row 2 of table A124530).

Original entry on oeis.org

1, 2, 7, 26, 107, 486, 2398, 12668, 70863, 416304, 2552490, 16254406, 107095090, 727834866, 5089682472, 36548625188, 269065010063, 2027942075946, 15630423416331, 123079853443384, 989356860469923, 8112792202324232
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Crossrefs

Cf. A124532; A124540 (table); other rows: A124531, A124543, A124544, A124545, A124546.

Programs

  • PARI
    {a(n)=local(R);R=vector(n+3,r,vector(n+3,c,1)); for(i=0,n+2,for(r=0,n+2,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[3])^2+O(x^(n+1)))[n+1]}

A124543 Row 3 of rectangular table A124540; equals the self-convolution cube of A124533 (row 3 of table A124530).

Original entry on oeis.org

1, 3, 15, 73, 369, 1959, 10912, 63543, 385341, 2424988, 15788469, 106075089, 733801709, 5217101283, 38060759175, 284533309380, 2177136417042, 17032924895739, 136129119703837, 1110507731328900, 9240322072954209
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Crossrefs

Cf. A124533; A124540 (table); other rows: A124531, A124542, A124544, A124545, A124546.

Programs

  • PARI
    {a(n)=local(R);R=vector(n+4,r,vector(n+4,c,1)); for(i=0,n+3,for(r=0,n+3,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[4])^3+O(x^(n+1)))[n+1]}

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^3 ]^3, where R_n(x) is the g.f. of row n in table A124540.

A124544 Row 4 of rectangular table A124540; equals the self-convolution 4th power of A124534 (row 4 of table A124530).

Original entry on oeis.org

1, 4, 26, 156, 939, 5764, 36248, 233900, 1549193, 10529052, 73390856, 524300728, 3836318617, 28731858368, 220121136396, 1724083566552, 13798004944813, 112773980097516, 940841899662784, 8008011665402152, 69505777613953576
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Crossrefs

Cf. A124534; A124540 (table); other rows: A124531, A124542, A124543, A124545, A124546.

Programs

  • PARI
    {a(n)=local(R);R=vector(n+5,r,vector(n+5,c,1)); for(i=0,n+4,for(r=0,n+4,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[5])^4+O(x^(n+1)))[n+1]}

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^4 ]^4, where R_n(x) is the g.f. of row n in table A124540.

A124545 Row 5 of rectangular table A124540; equals the self-convolution 5th power of A124535 (row 5 of table A124530).

Original entry on oeis.org

1, 5, 40, 285, 1995, 13976, 98665, 704810, 5107950, 37619020, 281850156, 2149737335, 16700012890, 132177206400, 1066116496055, 8764513792396, 73445461419380, 627378087294215, 5462723243482985, 48480560040789335
Offset: 0

Views

Author

Paul D. Hanna, Nov 05 2006

Keywords

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Crossrefs

Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124546.

Programs

  • PARI
    {a(n)=local(R);R=vector(n+6,r,vector(n+6,c,1)); for(i=0,n+5,for(r=0,n+5,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[6])^5+O(x^(n+1)))[n+1]}

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^5 ]^5, where R_n(x) is the g.f. of row n in table A124540.
Showing 1-10 of 17 results. Next

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