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A007472 Shifts 2 places left when binomial transform applied twice.
(Formerly M2812)
1
1, 1, 1, 3, 9, 29, 105, 431, 1969, 9785, 52145, 296155, 1787385, 11428949, 77124569, 546987143, 4062341601, 31502219889, 254500383457, 2137863653811, 18639586581097, 168387382189709, 1573599537048265, 15189509662516063, 151243491212611217, 1551565158004180137 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

MAPLE

bintr:= proc(p) local b;

          b:=proc(n) option remember; add (p(k)*binomial(n, k), k=0..n) end

        end:

b:= (bintr@@2)(a):

a:= n-> `if`(n<2, 1, b(n-2)):

seq (a(n), n=0..30);  # Alois P. Heinz, Oct 18 2012

MATHEMATICA

bintr[p_] := Module[{b}, b[n_] := b[n] = Sum [p[k]*Binomial[n, k], {k, 0, n}]; b]; b = a // bintr // bintr; a[n_] := If[n<2, 1, b[n-2]]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Jan 27 2014, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A136628 A151031 A151032 * A292756 A151451 A138938

Adjacent sequences:  A007469 A007470 A007471 * A007473 A007474 A007475

KEYWORD

nonn,nice,eigen

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 18 18:58 EDT 2018. Contains 316323 sequences. (Running on oeis4.)