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

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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.

A071747 Expansion of (1+x^4*C^2)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

Original entry on oeis.org

1, 2, 5, 14, 43, 136, 443, 1478, 5027, 17368, 60788, 215084, 768094, 2764880, 10021721, 36546310, 133990755, 493606680, 1826192640, 6782469540, 25278252810, 94512157680, 354397639830, 1332454176924, 5022040887822
Offset: 0

Views

Author

N. J. A. Sloane, Jun 06 2002

Keywords

Crossrefs

First differences of A067294.
Showing 1-2 of 2 results.

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

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