A007469 Shifts left 2 places under Stirling2 transform. (Formerly M1498)

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

1,4

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

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 *)

Crossrefs

Sequence in context: A268170 A000522 A182290 * A306026 A091139 A084785

Adjacent sequences: A007466 A007467 A007468 * A007470 A007471 A007472

Keyword

nonn,nice,eigen

Author

N. J. A. Sloane

Status

approved