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A122852 Row sums of number triangle A122851. 3
1, 1, 2, 3, 6, 11, 24, 51, 122, 291, 756, 1979, 5526, 15627, 46496, 140451, 442194, 1414931, 4687212, 15785451, 54764846, 193129659, 698978136, 2570480147, 9672977706, 36967490691, 144232455524, 571177352091, 2304843053382, 9434493132011, 39289892366736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Essentially the same as A072374. - R. J. Mathar, Jun 18 2008

Diagonal sums of A008279. - Paul Barry, Feb 11 2009

LINKS

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

Guo-Niu Han, Hankel Continued fractions and Hankel determinants of the Euler numbers, arXiv:1906.00103 [math.CO], 2019. See p. 27.

Qiong Qiong Pan, Jiang Zeng, The gamma-coefficients of Branden's (p,q)-Eulerian polynomials and André permutations, arXiv:1910.01747 [math.CO], 2019.

FORMULA

a(n) = Sum{k=0..n} C(k,n-k)*(n-k)!.

From Paul Barry, Feb 11 2009: (Start)

G.f.: 1/(1-x-x^2/(1-x^2/(1-x-2x^2/(1-2x^2/(1-x-3x^2/(1-3x^2/(1-x-4x^2/(1-4x^2/(1-... (continued fraction).

a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*k!. (End)

Conjecture: -2*a(n) + 3*a(n-1) + (n-1)*a(n-2) + (-n+1)*a(n-3) = 0. - R. J. Mathar, Nov 15 2012

a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 + 1/8) * n^((n+1)/2) / 2^(n/2+1) * (1 + 37/(48*sqrt(2*n))). - Vaclav Kotesovec, Feb 08 2014

MATHEMATICA

Table[Sum[Binomial[n-k, k]*k!, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)

CROSSREFS

Sequence in context: A047750 A072187 A072374 * A192573 A284994 A107113

Adjacent sequences:  A122849 A122850 A122851 * A122853 A122854 A122855

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 14 2006

EXTENSIONS

More terms from Vaclav Kotesovec, Jun 04 2019

STATUS

approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)