The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003659 Shifts left under Stirling2 transform. (Formerly M1681) 18
 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. Stirling2 transform of a(n) = [1, 1, 2, 6, 26, ...] is a(n+1) = [1, 2, 6, 26, ...]. Eigensequence of Stirling2 triangle A008277. - Philippe Deléham, Mar 23 2007 REFERENCES 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..330 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; 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] M. Janjic, Determinants and Recurrence Sequences, Journal of Integer Sequences, 2012, Article 12.3.5. [N. J. A. Sloane, Sep 16 2012] Istvan Mezo, On powers of Stirling matrices, arXiv:0812.4047 [math.CO], 2008. [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). G.f. satisfies: Sum_{n>=1} a(n)*x^n = x * (1 + Sum_{n>=1} a(n) * x^n / Product_{j=1..n} (1 - j*x)). - Ilya Gutkovskiy, May 09 2019 a(1) = 1; a(n+1) = Sum_{k=1..n} Stirling2(n,k) * a(k). - Seiichi Manyama, Jun 24 2022 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 */ (PARI) a_vector(n) = my(v=vector(n)); v[1]=1; for(i=1, n-1, v[i+1]=sum(j=1, i, stirling(i, j, 2)*v[j])); v; \\ Seiichi Manyama, Jun 24 2022 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 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 5 01:38 EST 2023. Contains 360082 sequences. (Running on oeis4.)