

A129952


Binomial transform of A124625.


9



1, 1, 2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288, 26624, 57344, 122880, 262144, 557056, 1179648, 2490368, 5242880, 11010048, 23068672, 48234496, 100663296, 209715200, 436207616, 905969664, 1879048192, 3892314112
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OFFSET

0,3


COMMENTS

Essentially the same as A057711: a(n) = A057711(n) for n >= 1.
Number of permutations of length n>=0 avoiding the partially ordered pattern (POP) {1>2, 1>3} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second and third elements.  Sergey Kitaev, Dec 08 2020


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Index entries for linear recurrences with constant coefficients, signature (4,4).


FORMULA

a(0) = 1, a(1) = 1; for n > 1, a(n) = n*2^(n2).
G.f.: (13*x+2*x^2+2*x^3)/(12*x)^2.
E.g.f.: (1/2)*(x*exp(2*x) + x + 2).  G. C. Greubel, Jun 08 2016


MATHEMATICA

LinearRecurrence[{4, 4}, {1, 1, 2, 6}, 30] (* G. C. Greubel, Jun 08 2016; corrected by Georg Fischer, Apr 02 2019 *)


PROG

(MAGMA) m:=15; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; [ &+[ Binomial(j1, k1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; // Klaus Brockhaus, Jun 17 2007
(PARI) {m=29; print1(1, ", ", 1, ", "); for(n=2, m, print1(n*2^(n2), ", "))} \\ Klaus Brockhaus, Jun 17 2007


CROSSREFS

Cf. A124625, A045623, A057711, A129953 (first differences), A129954 (second differences), A129955 (third differences).
Sequence in context: A078774 A174016 A265725 * A057711 A302239 A264551
Adjacent sequences: A129949 A129950 A129951 * A129953 A129954 A129955


KEYWORD

nonn,easy


AUTHOR

Paul Curtz, Jun 10 2007


EXTENSIONS

Edited and extended by Klaus Brockhaus, Jun 17 2007


STATUS

approved



