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A003659 Shifts left under Stirling-2 transform.
(Formerly M1681)
6
1, 1, 2, 6, 26, 152, 1144, 10742, 122772, 1673856, 26780972, 496090330, 10519217930, 252851833482, 6832018188414, 205985750827854, 6885220780488694, 253685194149119818, 10250343686634687424, 452108221967363310278, 21676762640915055856716 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Apart from leading term, number of M-sequences from multicomplexes on at most 4 variables with no monomial of degree more than n+1.

Stirling-2 transform of a(n) = [1, 1, 2, 6, 26, ...] is a(n+1) = [1, 2, 6, 26, ...].

Eigensequence of Stirling-2 triangle A008277. - Philippe Deléham, Mar 23 2007

REFERENCES

M. Janjic, Determinants and Recurrence Sequences, Journal of Integer Sequences, 2012, Article 12.3.5. - From N. J. A. Sloane, Sep 16 2012

S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.

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 = 1..130

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]

Istvan Mezo, On powers of Stirling matrices, Dec 21, 2008. [From Jonathan Vos Post, Dec 22 2008]

N. J. A. Sloane, Transforms

FORMULA

E.g.f. A(x) satisfies A(x)'=1+A(exp(x)-1).

MAPLE

stirtr:= proc(p)

           proc(n) add(p(k)*Stirling2(n, k), k=0..n) end

         end:

a:= proc(n) option remember; `if`(n<3, 1, aa(n-1)) end:

aa:= stirtr(a):

seq(a(n), n=1..25);  # Alois P. Heinz, Jun 22 2012

MATHEMATICA

terms = 21; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[Exp[x] - 1 + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms];

CoefficientList[A[x], x]*Range[0, terms]! // Rest (* _Jean-François Alcover, May 23 2012, updated Jan 12 2018 *)

PROG

(PARI) {a(n)=local(A, E); if(n<0, 0, A=O(x); E=exp(x+x*O(x^n))-1; for(m=1, n, A=intformal( subst( 1+A, x, E+x*O(x^m)))); n!*polcoeff(A, n))} /* Michael Somos, Mar 08 2004 */

CROSSREFS

Cf. A048801.

Cf. A153277, A153278. - Jonathan Vos Post, Dec 22 2008

Sequence in context: A000629 A185994 A032187 * A159602 A032271 A205502

Adjacent sequences:  A003656 A003657 A003658 * A003660 A003661 A003662

KEYWORD

nonn,nice,eigen

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified February 23 21:23 EST 2018. Contains 299588 sequences. (Running on oeis4.)