A001926 G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3]. (Formerly M4628 N1978)

1, 9, 46, 177, 571, 1632, 4270, 10446, 24244, 53942, 115954, 242240, 494087, 987503, 1939634, 3753007, 7167461, 13532608, 25293964, 46856332, 86110792, 157125052, 284866900, 513470464, 920659517, 1642844485, 2918680214, 5164483453, 9104522495, 15995633440

Offset

0,2

Comments

From rook polynomials.

References

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Links

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

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (7,-18,17,7,-24,9,9,-6,-1,1).

Maple

A001926:=-(1+z)**2/(z**2+z-1)**3/(z-1)**4; # conjectured (correctly) by Simon Plouffe in his 1992 dissertation

Mathematica

nn = 30; CoefficientList[Series[(1 + x)^2/((1 - x)^4 (1 - x - x^2)^3), {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *)
LinearRecurrence[{7, -18, 17, 7, -24, 9, 9, -6, -1, 1}, {1, 9, 46, 177, 571, 1632, 4270, 10446, 24244, 53942}, 30] (* Harvey P. Dale, Apr 30 2022 *)

Crossrefs

Second differences are in A002941.

Sequence in context: A201458 A034487 A035039 * A213749 A085385 A217152

Adjacent sequences: A001923 A001924 A001925 * A001927 A001928 A001929

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Apr 10 2009

Status

approved