A061889 a(n) = number of solutions to x_1 + x_2 + ... + x_n = x_{n+1} where each x_i is a factorial.

1, 1, 2, 2, 3, 2, 4, 3, 5, 5, 7, 8, 10, 8, 13, 14, 15, 18, 20, 23, 29, 31, 36, 41, 49, 54, 63, 72, 80, 92, 108, 116, 137, 153, 174, 197, 222, 250, 281, 318, 354, 398, 450, 497, 561, 624, 697, 779, 869, 964, 1075, 1193, 1325, 1471, 1635, 1809, 2004, 2217, 2455, 2711

Offset

2,3

Links

Table of n, a(n) for n=2..61.

Example

a[6]=3 since 5!+5!+5!+5!+5!+5!=6!, 3!+3!+3!+2!+2!+2!=4! and 1!+1!+1!+1!+1!+1!=3!

Mathematica

f[n_, k_, m_] := (* # of partitions of n into k factorials <= m! *) Which[n==k, 1, m<=1||n<k|| n>k m!, 0, True, f[n, k, m]=f[n, k, m-1]+f[n-m!, k-1, m]]; a[n_] := Sum[f[r!, n, r-1], {r, 2, n}];

Crossrefs

Sequence in context: A211316 A280226 A307995 * A240089 A218700 A325331

Adjacent sequences: A061886 A061887 A061888 * A061890 A061891 A061892

Keyword

nonn

Author

Erich Friedman, Jun 23 2001

Extensions

More terms from Dean Hickerson, Jun 25, 2001

Status

approved