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 A238314 Binomial transform of the squared rows of the table A072233 (A008284). 1

%I #10 Feb 27 2014 03:26:03

%S 1,1,3,7,33,91,388,1163,4231,13297,44694,136621,444535,1335335,

%T 4149785,12327698,37154245,108185961,318923590,913506701,2633793550,

%U 7443298426,21073435606,58715695683,163805615535,450730653566,1239947467778,3374934052348

%N Binomial transform of the squared rows of the table A072233 (A008284).

%H Vincenzo Librandi, <a href="/A238314/b238314.txt">Table of n, a(n) for n = 0..80</a>

%F a(n) = sum(binomial(n,k)*p(n,k)^2,k=0..n), where p(n,k) is the number of partitions of n into k positive parts (A072233, A008284).

%t pnkList[n_] := Table[Length[IntegerPartitions[n, {k}]], {k, 0, n}]

%t Table[Total[Table[Binomial[n,k],{k,0,n}] Map[#^2 &, pnkList[n]]], {n,0,40}]

%Y Cf. A072233, A008284.

%K nonn

%O 0,3

%A _Emanuele Munarini_, Feb 24 2014

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Last modified September 9 01:17 EDT 2024. Contains 375759 sequences. (Running on oeis4.)