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.

A105621 Column 2 of triangle A105620.

Original entry on oeis.org

1, -3, -7, -39, -315, -3243, -40167, -579159, -9514395, -175345083, -3582404487, -80368306119, -1964266364475, -51955106653323, -1478719724319207, -45062796853058679, -1463985729352297755, -50509695778598958363, -1844377821680825976327
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105620 is the matrix inverse square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(R,M=matrix(n+3,n+3,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<0,0,R[n+3,3]))}

A105622 Row sums of triangle A105620.

Original entry on oeis.org

1, 0, -3, -16, -104, -908, -9980, -130756, -1978044, -33864628, -646882700, -13637768276, -314550050684, -7879500818548, -213050486593260, -6184793428783156, -191870459680722524, -6335136849263878868, -221817478808912340620, -8209644712019737332436
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105620 is the matrix inverse square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(R,M=matrix(n+3,n+3,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<0,0,sum(k=0,n,R[n+1,k+1])))}

A105628 Row sums of triangle A105626.

Original entry on oeis.org

1, 4, 25, 208, 2152, 26524, 378700, 6142948, 111593932, 2244992404, 49561796380, 1191625266388, 31001841211852, 867899276874964, 26017959787456060, 831650920910208628, 28237504357447540972, 1014987937635390612724
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105626 equals the cube of the matrix square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(R,M=matrix(n+3,n+3,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-3); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<0,0,sum(k=0,n,R[n+1,k+1])))}

A105630 Column 0 of triangle A105629, which is the matrix logarithm of triangle A105623.

Original entry on oeis.org

0, 1, 3, 17, 135, 1353, 16251, 226857, 3605775, 64288209, 1270969971, 27603549057, 653517822615, 16755529944729, 462601460800491, 13685474246611737, 431948067953729055, 14489465807596684449, 514794897939436455651
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105623 equals the matrix square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-1); L=sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i); return(if(n<0,0,L[n+1,1]/2))}

A105631 Row sums of triangle A105629, which is the matrix logarithm of triangle A105623.

Original entry on oeis.org

0, 1, 5, 27, 195, 1833, 21125, 286451, 4453859, 78031153, 1520668645, 32631020011, 764640901539, 19431070911513, 532315915981605, 15640217893829891, 490640673319698179, 16368499360721508833, 578693283962999831365
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105623 equals the matrix square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-1); L=sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i); return(if(n<0,0,sum(k=0,n,L[n+1,k+1])/2))}

A105624 Column 2 of triangle A105623.

Original entry on oeis.org

1, 3, 19, 167, 1831, 23843, 358339, 6097607, 115840951, 2430329603, 55812650419, 1392737182247, 37528377195271, 1086086115808163, 33600297897404899, 1106632150406054087, 38659524289511283991, 1427864216163041265923
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105623 equals the matrix square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(R,M=matrix(n+3,n+3,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-1); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<0,0,R[n+3,3]))}

A105625 Row sums of triangle A105623.

Original entry on oeis.org

1, 2, 7, 40, 324, 3336, 41192, 590480, 9623944, 175703056, 3552295752, 78802665120, 1903505233064, 49743146641616, 1398474578414632, 42092742475096960, 1350629892258170184, 46025643554111478576
Offset: 0

Views

Author

Paul D. Hanna, Apr 16 2005

Keywords

Comments

A105623 equals the matrix square-root of triangle A105615.

Crossrefs

Programs

  • PARI
    {a(n)=local(R,M=matrix(n+3,n+3,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-1); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<0,0,sum(k=0,n,R[n+1,k+1])))}
Previous Showing 11-17 of 17 results.