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.

A125807 Central terms of odd-indexed rows of triangle A125806: a(n) = A125806(2n+1,n).

Original entry on oeis.org

1, 3, 16, 119, 1070, 10762, 116546, 1330923, 15823388, 194168612, 2444224858, 31422225930, 411141476444, 5460849893348, 73474839110524, 999764999592077, 13738614091375204, 190450074950481408, 2660727794475865450
Offset: 0

Views

Author

Paul D. Hanna, Dec 12 2006

Keywords

Comments

Central terms of even-indexed rows of triangle A125806 equal A063075 (number of partitions of 2n^2 whose Ferrers-plot fits within a 2n X 2n box and cover an n X n box).

Crossrefs

Cf. A125806 (triangle); A063075; A125808, A125809 (row sums).

Programs

  • PARI
    {a(n)=local(C_q=if(n==0,1,prod(j=n+2,2*n+1,1-q^j)/prod(j=1,n,1-q^j))); sum(i=0,(n+1)*n,polcoeff(C_q,i)^2)}

A125808 Adjacent-to-central terms of even-indexed rows of triangle A125806: a(n) = A125806(2n+2,n).

Original entry on oeis.org

1, 4, 29, 256, 2592, 28160, 322873, 3850352, 47369432, 597565304, 7695966346, 100852014156, 1341310032320, 18067954497864, 246098396499471, 3384883529933828, 46960152641672616, 656538880287562528
Offset: 0

Views

Author

Paul D. Hanna, Dec 12 2006

Keywords

Comments

Central terms of even-indexed rows of triangle A125806 equal A063075 (number of partitions of 2n^2 whose Ferrers-plot fits within a 2n X 2n box and cover an n X n box).

Crossrefs

Cf. A125806 (triangle); A063075; A125807, A125809 (row sums).

Programs

  • PARI
    {a(n)=local(C_q=if(n==0,1,prod(j=n+3,2*n+2,1-q^j)/prod(j=1,n,1-q^j))); sum(i=0,(n+2)*n,polcoeff(C_q,i)^2)}

A125809 Row sums of triangle A125806.

Original entry on oeis.org

1, 2, 4, 8, 18, 44, 120, 348, 1064, 3368, 10952, 36336, 122570, 419104, 1449672, 5064240, 17844558, 63356072, 226459120, 814323856, 2944055592, 10695723368, 39029679176, 142998497292, 525862368660, 1940381764088, 7182278240848
Offset: 0

Views

Author

Paul D. Hanna, Dec 12 2006

Keywords

Comments

Triangle A125806 gives the sum of squared coefficients of q in the corresponding q-binomial coefficients.

Crossrefs

Cf. A125806 (triangle); A063075, A125807, A125808.

Programs

  • PARI
    {a(n)=sum(k=0,n,sum(i=0,(n-k)*k, polcoeff(if(n==0,1,prod(j=n-k+1,n,1-q^j)/prod(j=1,k,1-q^j)),i)^2))}
Showing 1-3 of 3 results.