cp's OEIS Frontend

A157391 A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).

%I A157391 #6 Feb 12 2023 10:20:37
%S A157391 1,1,1,1,3,0,1,9,0,0,1,25,0,0,0,1,75,0,0,0,0,1,231,0,0,0,0,0,1,763,0,
%T A157391 0,0,0,0,0,1,2619,0,0,0,0,0,0,0,1,9495,0,0,0,0,0,0,0,0,1,35695,0,0,0,
%U A157391 0,0,0,0,0,0,1,140151
%N A157391 A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
%C A157391 Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 1,
%C A157391 summed over parts with equal biggest part (see the Luschny link).
%C A157391 Underlying partition triangle is A144357.
%C A157391 Same partition product with length statistic is A049403.
%C A157391 Diagonal a(A000217(n)) = falling_factorial(1,n-1), row in A008279.
%C A157391 Row sum is A000085.
%H A157391 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html">Counting with Partitions</a>.
%H A157391 Peter Luschny, <a href="http://www.luschny.de/math/seq/stirling1partitions.html">Generalized Stirling_1 Triangles</a>.
%F A157391 T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
%F A157391 T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
%F A157391 1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
%F A157391 f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n+3).
%Y A157391 Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395
%K A157391 easy,nonn,tabl
%O A157391 1,5
%A A157391 _Peter Luschny_, Mar 07 2009, Mar 14 2009