Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
A007470
Shifts left when Stirling2 transform is applied twice.
(Formerly M2979)
1
1, 1, 3, 14, 97, 934, 11814, 188650, 3698399, 87133235, 2424143590, 78483913829, 2920947798710, 123676552368689, 5904927996501989, 315465738505181316, 18730636267115299571, 1228583480023634860711, 88548597460914590753663, 6979070787198903764535472
OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
stirtr:= proc(p)
proc(n) add(p(k)*Stirling2(n, k), k=0..n) end
end:
a:= proc(n) option remember; `if`(n<2, 1, aa(n-1)) end:
aa:= (stirtr@@2)(a):
seq(a(n), n=1..25); # Alois P. Heinz, Jun 22 2012
MATHEMATICA
stirtr[p_] := Function[{n}, Sum[p[k]*StirlingS2[n, k], {k, 0, n}]]; a[n_] := a[n] = If[n < 2, 1, aa[n-1]]; aa := stirtr[stirtr[a]]; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Oct 30 2013, translated from Alois P. Heinz's Maple program *)
CROSSREFS
Sequence in context: A345106 A276747 A367383 * A306986 A074515 A336947
KEYWORD
nonn,nice,eigen
STATUS
approved