login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000800 Sum of upward diagonals of Eulerian triangle. 6
1, 1, 1, 2, 5, 13, 38, 125, 449, 1742, 7269, 32433, 153850, 772397, 4088773, 22746858, 132601933, 807880821, 5132235182, 33925263901, 232905588441, 1657807491222, 12215424018837, 93042845392105, 731622663432978, 5931915237693517 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 254.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 215.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 1/(1-x/(1-x^2/(1-2x/(1-2x^2/(1-3x/(1-3x^2/(1-... (continued fraction). [Paul Barry, Mar 24 2010]

a(n) = Sum_{k} A173018(n-k, k) - Michael Somos, Mar 17 2011

G.f.: 1/Q(0), where Q(k)= 1 - x*(k+1)/(1 - x^2*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 14 2013

G.f.: 1/Q(0), where Q(k)=  1 - x - x*(x+1)*k - x^3*(k+1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 14 2013

EXAMPLE

1 = 1, 1 = 1, 1 = 1 + 0, 2 = 1 + 1, 5 = 1 + 4 + 0, etc.

1 + x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 38*x^6 + 125*x^7 + 449*x^8 + 1742*x^9 + ...

MATHEMATICA

t[n_ /; n >= 0, 0] = 1; t[n_, k_] /; k < 0 || k > n = 0; t[n_, k_] := t[n, k] = (n-k)*t[n-1, k-1] + (k+1)*t[n-1, k]; a[n_] := Sum[t[n-k, k], {k, 0, n}]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Dec 14 2011, after Michael Somos *)

CROSSREFS

Cf. A173018.

Sequence in context: A148303 A148304 A149859 * A149860 A006823 A151446

Adjacent sequences:  A000797 A000798 A000799 * A000801 A000802 A000803

KEYWORD

nonn,easy,nice

AUTHOR

Tony Harkin [ harkin(AT)mit.edu, tharkin(AT)vortex.weather.brockport.edu ]

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

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

Last modified December 22 07:03 EST 2014. Contains 252328 sequences.