A107672 Column 0 of triangle A107671.

1, 8, 513, 81856, 23846125, 10943504136, 7250862593527, 6545029128786432, 7720335872745730749, 11531675416606553251000, 21278751956820661358187902, 47547062997060115956475702656, 126548714317113405123981003974183

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = (n+1)^3*A107673(n). [Corrected by Petros Hadjicostas, Mar 11 2021]

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

Prog

(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]}

Crossrefs

Cf. A107671, A107673, A107676.

Sequence in context: A067512 A067505 A173058 * A091112 A015480 A159532

Adjacent sequences: A107669 A107670 A107671 * A107673 A107674 A107675

Keyword

nonn

Author

Paul D. Hanna, Jun 07 2005

Status

approved