A007469 Shifts left 2 places under Stirling2 transform.

1, 1, 1, 2, 5, 16, 66, 343, 2167, 16193, 140919, 1414947, 16258868, 211935996, 3105828560, 50748310068, 918138961643, 18287966027343, 399145502051200, 9505803743367971, 246064556796896554, 6897674469134480653, 208651954748397405264, 6788671409470892058148

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen

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..150
• 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

Programs

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-2)) end:
aa:= stirtr(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<3, 1, aa[n-2]]; aa = stirtr[a]; Table[a[n], {n, 1, 24}] (* Jean-François Alcover, Jan 09 2013, translated from Alois P. Heinz's Maple program *)