A038561 Left-hand border of triangle A046937.

1, 2, 3, 8, 24, 83, 324, 1400, 6609, 33758, 185136, 1083233, 6726366, 44130128, 304741623, 2207682188, 16729947276, 132281116715, 1088831511000, 9311082630620, 82569723552561, 758057178490082, 7194283782101844, 70481938088367569

Offset

0,2

Comments

For n>1: a(n) is the number of entries in the last blocks of all set partitions of [n]. a(3) = 8 because the number of entries in the last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 3+1+1+2+1 = 8. - Alois P. Heinz, May 08 2017

References

H. W. Gould, A linear binomial recurrence and the Bell numbers and polynomials, preprint, 1998

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..500

R. K. Guy, Letters to N. J. A. Sloane, June-August 1968

Formula

G.f. A(x) satisfies: A(x) = 1 + x * (1 + A(x/(1 - x)) / (1 - x)). - Ilya Gutkovskiy, Jun 30 2020

Maple

A038561List := proc(m) local A, P, n; A := [1, 2]; P := [1];
for n from 1 to m - 2 do P := ListTools:-PartialSums([A[-1], op(P)]);
A := [op(A), P[-1]] od; A end: A038561List(24); # Peter Luschny, Mar 24 2022

Mathematica

a[0, 0] = 1; a[1, 0] = 2; a[n_, 0] := a[n-1, n-1]; a[n_, k_] := a[n, k] = a[n, k-1] + a[n-1, k-1]; a[n_] := a[n, 0]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 06 2013 *)

Prog

(Haskell)
a038561 = head . a046937_row  -- Reinhard Zumkeller, Jan 06 2014

Crossrefs

A040027(n) + B(n), where B(n) = Bell numbers A000110.

Related to A000110, A040027, A038559, A038560.

Column k=1 of A286416 (for n>1).

Sequence in context: A331874 A089847 A304121 * A055981 A182212 A120260

Adjacent sequences: A038558 A038559 A038560 * A038562 A038563 A038564

Keyword

nonn,nice,easy

Author

Henry Gould, N. J. A. Sloane

Status

approved