A006637 From generalized Catalan numbers. (Formerly M5005)

16, 96, 344, 952, 2241, 4712, 9108, 16488, 28314, 46552, 73788, 113360, 169507, 247536, 354008, 496944, 686052, 932976, 1251568, 1658184, 2172005, 2815384, 3614220, 4598360, 5802030, 7264296, 9029556, 11148064, 13676487, 16678496

Offset

0,1

References

H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: (2-x)^4/(x-1)^8. - Sean A. Irvine, May 31 2017

a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8). - Wesley Ivan Hurt, Jun 18 2022

Crossrefs

Cf. A181289.

Sequence in context: A277044 A192037 A143060 * A241937 A014344 A239613

Adjacent sequences: A006634 A006635 A006636 * A006638 A006639 A006640

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

a(6) and a(8) corrected and more terms from Sean A. Irvine, May 31 2017

Status

approved