A111826 Number of partitions of 5*6^n into powers of 6, also equals column 1 of triangle A111825, which shifts columns left and up under matrix 6th power.

1, 6, 96, 6306, 1883076, 2700393702, 19324893252552, 709398600017820522, 136347641698786289641932, 139389318443495655514432423662, 767442745549858935398537400096197328

Offset

0,2

Comments

Let q=6; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Formula

a(n) = [x^(5*6^n)] 1/Product_{j>=0}(1-x^(6^j)).

Prog

(PARI) a(n, q=6)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+2, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i || j==1, B[i, j]=1, B[i, j]=(A^q)[i-1, j-1]); )); A=B); return(A[n+2, 2]))

Crossrefs

Cf. A111825 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111831 (q=7), A111836 (q=8).

Sequence in context: A126151 A066319 A186269 * A213797 A285025 A288544

Adjacent sequences: A111823 A111824 A111825 * A111827 A111828 A111829

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved