A218566 Triangle T[r,c]=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c), read by rows.

0, 1, 3, 2, 12, 240, 3, 27, 1080, 226800, 4, 48, 2880, 1209600, 3657830400, 5, 75, 6000, 3780000, 22861440000, 1267438233600000, 6, 108, 10800, 9072000, 82301184000, 9125555281920000, 11274806061917798400000

Offset

1,3

Comments

T[b,d] gives the number of positive numbers that can be written in base b with d(d+1)/2 digits such that for each k=1,...,d some digit appears exactly k times, cf. A218560, A167819, A218556 and related sequences.

Links

Table of n, a(n) for n=1..28.

Formula

T[r,1] = r-1. T[r,2] = 3(r-1)^2. T[r,3] = 60(r-2)(r-1)^2, etc.

Example

The first 6 rows of the triangle are:
r=1: 0;
r=2: 1, 3;
r=3: 2, 12,  240;
r=4: 3, 27,  1080,  226800;
r=5: 4, 48,  2880,  1209600,  3657830400;
r=6: 5, 75,  6000,  3780000,  22861440000,  1267438233600000.
Row 2 counts the numbers 1 and 4=100[2], 5=101[2], 6=110[2].
Row 3 counts the numbers {1, 2} and {9=100[3], 10=101[3], 12=110[3], 14=112[3], 16=121[3], ..., 25=221[3]} and {248=100012[3], ..., 714=222110[3]}.

Prog

(PARI) T(r, c)=(r-1)*binomial(r-1, c-1)*(c-1)!*A093883(c)

Crossrefs

Sequence in context: A189736 A025232 A236435 * A125135 A055456 A198303

Adjacent sequences: A218563 A218564 A218565 * A218567 A218568 A218569

Keyword

nonn,tabl

Author

M. F. Hasler, Nov 02 2012

Status

approved