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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Essentially the same as A057711: a(n) = A057711(n) for n >= 1.

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.

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^(n-2).

G.f.: (1-3*x+2*x^2+2*x^3)/(1-2*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(j-1, k-1)*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^(n-2), ", "))} \\ 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

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Last modified May 22 04:02 EDT 2019. Contains 323473 sequences. (Running on oeis4.)