A007470 Shifts left when Stirling2 transform is applied twice. (Formerly M2979)

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

Alois P. Heinz, Table of n, a(n) for n = 1..120

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

Adjacent sequences: A007467 A007468 A007469 * A007471 A007472 A007473

Keyword

nonn,nice,eigen

Author

N. J. A. Sloane

Status

approved