cp's OEIS Frontend

A038561 Left-hand border of triangle A046937.

%I A038561 #24 Mar 24 2022 18:48:55
%S A038561 1,2,3,8,24,83,324,1400,6609,33758,185136,1083233,6726366,44130128,
%T A038561 304741623,2207682188,16729947276,132281116715,1088831511000,
%U A038561 9311082630620,82569723552561,758057178490082,7194283782101844,70481938088367569
%N A038561 Left-hand border of triangle A046937.
%C A038561 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
%D A038561 H. W. Gould, A linear binomial recurrence and the Bell numbers and polynomials, preprint, 1998
%H A038561 Reinhard Zumkeller, <a href="/A038561/b038561.txt">Table of n, a(n) for n = 0..500</a>
%H A038561 R. K. Guy, <a href="/A002186/a002186.pdf">Letters to N. J. A. Sloane, June-August 1968</a>
%F A038561 G.f. A(x) satisfies: A(x) = 1 + x * (1 + A(x/(1 - x)) / (1 - x)). - _Ilya Gutkovskiy_, Jun 30 2020
%p A038561 A038561List := proc(m) local A, P, n; A := [1,2]; P := [1];
%p A038561 for n from 1 to m - 2 do P := ListTools:-PartialSums([A[-1], op(P)]);
%p A038561 A := [op(A), P[-1]] od; A end: A038561List(24); # _Peter Luschny_, Mar 24 2022
%t A038561 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 *)
%o A038561 (Haskell)
%o A038561 a038561 = head . a046937_row  -- _Reinhard Zumkeller_, Jan 06 2014
%Y A038561 A040027(n) + B(n), where B(n) = Bell numbers A000110.
%Y A038561 Related to A000110, A040027, A038559, A038560.
%Y A038561 Column k=1 of A286416 (for n>1).
%K A038561 nonn,nice,easy
%O A038561 0,2
%A A038561 _Henry Gould_, _N. J. A. Sloane_