

A104858


Partial sums of the little Schroeder numbers (A001003).


3



1, 2, 5, 16, 61, 258, 1161, 5440, 26233, 129282, 648141, 3294864, 16943733, 87983106, 460676625, 2429478144, 12893056497, 68802069506, 368961496469, 1987323655056, 10746633315501, 58321460916482, 317537398625945
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OFFSET

0,2


COMMENTS

The subsequence of primes begins: 2, 5, 61, no more through a(30). [Jonathan Vos Post, Feb 12 2010]


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200
GuoNiu Han, Enumeration of Standard Puzzles
GuoNiu Han, Enumeration of Standard Puzzles [Cached copy]


FORMULA

G.f.=[1+zsqrt(16z+z^2)]/[4z(1z)].
Recurrence: (n+1)*a(n) = (7*n2)*a(n1)  (7*n5)*a(n2) + (n2)*a(n3).  Vaclav Kotesovec, Oct 17 2012
a(n) ~ sqrt(24+17*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)).  Vaclav Kotesovec, Oct 17 2012
Define a triangle T(n,1) = T(n,n) = 1 for n = 1, 2, 3... and all other elements by T(r,c) = T(r,c1) + T(r1,c1) + T(r1,c). Its second column is A005408, its third column is A059993, and the sum of all terms in its row n is a(n1).  J. M. Bergot, Dec 01 2012


MAPLE

G:=(1+zsqrt(16*z+z^2))/4/z/(1z): Gser:=series(G, z=0, 29): 1, seq(coeff(Gser, z^n), n=1..27);


MATHEMATICA

CoefficientList[Series[(1+xSqrt[16*x+x^2])/4/x/(1x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)


CROSSREFS

Cf. A001003.
Sequence in context: A012051 A012159 A009736 * A303058 A322616 A178123
Adjacent sequences: A104855 A104856 A104857 * A104859 A104860 A104861


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Apr 24 2005


STATUS

approved



