A111821 Number of partitions of 4*5^n into powers of 5, also equals column 1 of triangle A111820, which shifts columns left and up under matrix 5th power.

1, 5, 55, 2055, 291430, 165397680, 390075741430, 3927972221522680, 172358768282285194555, 33479766506261422878944555, 29150234311482124092454001991430

Offset

0,2

Comments

Let q=5; 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^(4*5^n)] 1/Product_{j>=0}(1-x^(5^j)).

Prog

(PARI) a(n, q=5)=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. A111820 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111826 (q=6), A111831 (q=7), A111836 (q=8).

Sequence in context: A126157 A176267 A105715 * A275546 A068666 A082780

Adjacent sequences: A111818 A111819 A111820 * A111822 A111823 A111824

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved