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A218566 Triangle T[r,c]=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c), read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 21 00:08 EST 2019. Contains 329348 sequences. (Running on oeis4.)