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.

A067295 Fourth column of triangle A028364.

Original entry on oeis.org

14, 28, 76, 227, 715, 2333, 7810, 26663, 92456, 324700, 1152464, 4127294, 14895145, 54115895, 197764350, 726473055, 2680979820, 9934884960, 36953107320, 137913387450, 516295313430, 1938260223354
Offset: 0

Views

Author

Wolfdieter Lang, Feb 05 2002

Keywords

Crossrefs

Cf. A067294 (third column), A067296 (fifth column).

Formula

a(n)= A028364(n+3, 3) = C(0)*C(n+3)+C(1)*C(n+2)+C(2)*C(n+1)+ C(3)*C(n), with the Catalan numbers C(n)=A000108(n).
a(n)= (3*(31*n^3+163*n^2+254*n+112)/(8*(2*n+1)*(2*n+3)*(2*n+5)))*C(n+3).
G.f.: (c3(x)*c(x)-(c3(x)-1)/x)/x^3, with c3(x) := 1+x+2*x^2+5*x^3 and c(x) G.f. for Catalan numbers A000108.

A116869 Sixth column of triangle A028364.

Original entry on oeis.org

132, 297, 869, 2739, 8986, 30275, 104006, 362738, 1280592, 4566642, 16423581, 59497075, 216901454, 795117015, 2929034130, 10837075830, 40253156520, 150045410430, 561097823490, 2104382963214, 7913603390196
Offset: 0

Views

Author

Wolfdieter Lang, Mar 24 2006

Keywords

Comments

Also sixth diagonal of triangle A067323.

Crossrefs

Cf. A067296 (fifth column).

Formula

a(n)= A028364(n+5,5) = sum(C(k)*C(n+5-k),k=0..5), with the Catalan numbers C(n):=A000108(n).
G.f.: (c5(x)*c(x)-(c5(x)-1)/x)/x^5, with c5(x) := sum(C(k)*x^k, k=0..5) and c(x) is the g.f. for the Catalan numbers A000108.
Showing 1-2 of 2 results.

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

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