login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Column 0 of triangle A107671.
2

%I #11 Mar 11 2021 04:37:19

%S 1,8,513,81856,23846125,10943504136,7250862593527,6545029128786432,

%T 7720335872745730749,11531675416606553251000,

%U 21278751956820661358187902,47547062997060115956475702656,126548714317113405123981003974183

%N Column 0 of triangle A107671.

%F a(n) = (n+1)^3*A107673(n). [Corrected by _Petros Hadjicostas_, Mar 11 2021]

%F a(n) = Sum_{r=1..(n+1)} (-1)^(r-1) * Sum_{s_1, ..., s_r} (s_1^(-1)/(Product_{j=1..r} s_j!)) * Product_{j=1..r} (Sum_{i=1..j} s_i)^(3*s_j)), where the second sum is over lists (s_1, ..., s_r) of positive integers s_i such that Sum_{i=1..r} s_i = n + 1. (Thus, the second sum is over all compositions of n + 1.) - _Petros Hadjicostas_, Mar 11 2021

%o (PARI) {a(n)=local(P=matrix(n+1,n+1,r,c,if(r>=c,(r^3)^(r-c)/(r-c)!)), D=matrix(n+1,n+1,r,c,if(r==c,r)));(P^-1*D*P)[n+1,1]}

%Y Cf. A107671, A107673, A107676.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 07 2005