cp's OEIS Frontend

A014326 Convolution of partition numbers and Bell numbers.

%I A014326 #18 Jan 09 2023 02:23:11
%S A014326 1,2,5,12,32,95,328,1294,5748,28152,149768,856130,5218107,33712600,
%T A014326 229800588,1646316230,12355374717,96861192976,791258805462,
%U A014326 6720627186126,59234364203973,540812222400025,5106663817693176,49798678281859244,500857393911224861
%N A014326 Convolution of partition numbers and Bell numbers.
%H A014326 Alois P. Heinz, <a href="/A014326/b014326.txt">Table of n, a(n) for n = 0..500</a>
%p A014326 with(combinat):
%p A014326 a:= n-> add(numbpart(k)*bell(n-k), k=0..n):
%p A014326 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 15 2015
%t A014326 a[n_]:= Sum[PartitionsP[k]*BellB[n-k], {k,0,n}];
%t A014326 Table[a[n], {n,0,30}] (* _Jean-François Alcover_, Dec 06 2016 *)
%o A014326 (Magma)
%o A014326 A014326:= func< n | (&+[NumberOfPartitions(j)*Bell(n-j): j in [0..n]]) >;
%o A014326 [A014326(n): n in [0..40]]; // _G. C. Greubel_, Jan 08 2023
%o A014326 (SageMath)
%o A014326 def A014326(n): return sum(number_of_partitions(j)*bell_number(n-j) for j in range(n+1))
%o A014326 [A014326(n) for n in range(41)] # _G. C. Greubel_, Jan 08 2023
%Y A014326 Cf. A000041, A000110.
%Y A014326 Partial sums of A292503.
%K A014326 nonn
%O A014326 0,2
%A A014326 _N. J. A. Sloane_