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 1-4 of 4 results.

A166906 Column 1 of triangle A166905.

Original entry on oeis.org

1, 4, 33, 380, 5510, 95732, 1933288, 44437080, 1144564278, 32638644236, 1020503373032, 34708182795156, 1275532011982176, 50365443858930384, 2126358227959866224, 95577781657788563192, 4556923094838105968302
Offset: 0

Views

Author

Paul D. Hanna, Nov 28 2009

Keywords

Comments

Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).

Crossrefs

Cf. A166905, A158831, A166907, A166908, A166909.

Programs

  • PARI
    {a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+4))), M, N, P, m=n); M=matrix(m+3, m+3, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); N=matrix(m+2, m+2, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); P=matrix(m+2, m+2, r, c, M[r+1, c]); (P~*N~^-1)[n+2, 2]}

A166907 Column 2 of triangle A166905.

Original entry on oeis.org

1, 9, 108, 1610, 28560, 586320, 13658904, 355787568, 10243342296, 322939137312, 11063339361360, 409194048521778, 16249995494795920, 689585033717023224, 31140529927119263136, 1490994828293677370148, 75444108490820383882392
Offset: 0

Views

Author

Paul D. Hanna, Nov 28 2009

Keywords

Comments

Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).

Crossrefs

Cf. A166905, A158831, A166906, A166908, A166909.

Programs

  • PARI
    {a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+5))), M, N, P, m=n); M=matrix(m+4, m+4, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+4)))); polcoeff(F, c)); N=matrix(m+3, m+3, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+4)))); polcoeff(F, c)); P=matrix(m+3, m+3, r, c, M[r+1, c]); (P~*N~^-1)[n+3, 3]}

A166908 Column 3 of triangle A166905.

Original entry on oeis.org

1, 16, 270, 5148, 110929, 2677008, 71648322, 2107966432, 67649839664, 2352412120760, 88122951915388, 3538364803586104, 151611580761978784, 6905283671128114400, 333151832685664811338, 16973306740660778801468
Offset: 0

Views

Author

Paul D. Hanna, Nov 28 2009

Keywords

Comments

Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).

Crossrefs

Cf. A166905, A158831, A166906, A166907, A166909.

Programs

  • PARI
    {a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+6))), M, N, P, m=n); M=matrix(m+5, m+5, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+5)))); polcoeff(F, c)); N=matrix(m+4, m+4, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+5)))); polcoeff(F, c)); P=matrix(m+4, m+4, r, c, M[r+1, c]); (P~*N~^-1)[n+4, 4]}

A166909 Row sums of triangle A166905.

Original entry on oeis.org

1, 2, 11, 97, 1145, 16796, 293623, 5950792, 137075837, 3535416136, 100902444181, 3156570232069, 107392381479683, 3947409366073512, 155880018189733841, 6581149438442041483, 295807451972657856921, 14102499966460374953016
Offset: 0

Views

Author

Paul D. Hanna, Nov 28 2009

Keywords

Comments

Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).

Crossrefs

Cf. A166905, A158831, A166906, A166907, A166908.

Programs

  • PARI
    {a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+3))), M, N, P, m=n); M=matrix(m+2, m+2, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); P=matrix(n+1, n+1, r, c, M[r+1, c]); M=(P~*N~^-1); sum(k=1,n+1,M[n+1,k])}
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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