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 1-2 of 2 results.

A067294 Third column of triangle A028364.

Original entry on oeis.org

5, 9, 23, 66, 202, 645, 2123, 7150, 24518, 85306, 300390, 1068484, 3833364, 13855085, 50401395, 184392150, 677998830, 2504191470, 9286661010, 34564913820, 129077071500, 483474711330, 1815928888254
Offset: 0

Views

Author

Wolfdieter Lang, Feb 05 2002

Keywords

Comments

The first two columns give: A000108 (Catalan) and A005807. The next two columns give: A067295-6.

Crossrefs

First differences are in A071747.

Formula

a(n)= A028364(n+2, 2) = C(0)*C(n+2)+C(1)*C(n+1)+C(2)*C(n), with the Catalan numbers C(n)=A000108(n). a(n)= ((11*n^2+28*n+15)/(2*(2*n+1)*(2*n+3)))*C(n+2).
G.f.: (c2(x)*c(x)-(c2(x)-1)/x)/x^2, with c2(x) := 1+x+2*x^2 and c(x) G.f. for Catalan numbers A000108.

A067296 Fifth column of triangle A028364.

Original entry on oeis.org

42, 90, 255, 785, 2529, 8398, 28511, 98462, 344720, 1220532, 4362438, 15718149, 57028063, 208164950, 763915215, 2816707650, 10429892340, 38768134380, 144600329250, 541036998090, 2030157909234, 7637910332556
Offset: 0

Views

Author

Wolfdieter Lang, Feb 05 2002

Keywords

Crossrefs

Cf. A067295 (fourth column).

Formula

a(n)= A028364(n+4, 4) = sum(C(k)C(n+4-k), k=0..4), with the Catalan numbers C(n)=A000108(n).
a(n)= ((193n^4+1727*n^3+5303*n^2+6457*n+2520)/(8*(2*n+1)*(2*n+3)*(2*n+5)*(2*n+7)))*C(n+4).
G.f.: (c4(x)*c(x)-(c4(x)-1)/x)/x^4, with c4(x) := sum(C(k)*x^k, k=0..4) and c(x) g.f. for Catalan numbers A000108.
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.