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A091962 From enumerating paths in the plane. 5
0, 1, 42, 594, 4719, 26026, 111384, 395352, 1215126, 3331251, 8321170, 19240650, 41683005, 85408596, 166768096, 312203232, 563178924, 982981701, 1665911754, 2749500754, 4430505387, 6985558206, 10797503640, 16388608600, 24462014850, 35952994935, 52091785746 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

M. de Sainte Catherine, Couplages et Pfaffiens en Combinatoire, Physique et Informatique. Ph. D. Dissertation, Universite de Bordeaux 1, 1983.

R. P. Stanley, Enumerative Combinatorics, volume 1 (1986), p. 221, Example 4.5.18.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected with lattice paths, European J. Combin., 2 (1981), 55-60.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = binomial(2n+6, 7)*(2n+3)*(n+1)*(n+2)/240.

G.f.: x*(1+31*x+187*x^2+330*x^3+187*x^4+31*x^5+x^6)/(1-x)^11. [Colin Barker, May 07 2012]

MATHEMATICA

LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 1, 42, 594, 4719, 26026, 111384, 395352, 1215126, 3331251, 8321170}, 30] (* Harvey P. Dale, Apr 15 2017 *)

PROG

(PARI) a(n) = binomial(2*n+6, 7)*(2*n+3)*(n+1)*(n+2)/240; \\ Michel Marcus, Oct 13 2016

CROSSREFS

Cf. A006858.

Sequence in context: A245874 A279888 A104901 * A269659 A007746 A200853

Adjacent sequences:  A091959 A091960 A091961 * A091963 A091964 A091965

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Mar 13 2004

STATUS

approved

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Last modified August 16 08:52 EDT 2017. Contains 290623 sequences.