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A178473 For n>=0, let n!^(4) = A202369(n+1) and, for 0<=m<=n, C^(4)(n,m) = n!^(4)/(m!^(4)*(n-m)!^(4)). The sequence gives triangle of numbers C^(4)(n,m) with rows of length n+1. 2
1, 1, 1, 1, 2, 1, 1, 273, 273, 1, 1, 68, 9282, 68, 1, 1, 55, 1870, 1870, 55, 1, 1, 546, 15015, 3740, 15015, 546, 1, 1, 29, 7917, 1595, 1595, 7917, 29, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Conjecture. If p is prime of the form 4*k+1, then the k-th row contains two 1's and k-1 numbers multiple of p; if p is prime of the form 4*k+3, then the (2*k+1)-th row contains two 1's and 2*k numbers multiple of p.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Conjecture. A007814(C^(4)(n,m)) = A007814(C(n,m)).

EXAMPLE

Triangle begins

n/m.|..0.....1.....2.....3.....4.....5.....6.....7

==================================================

.0..|..1

.1..|..1......1

.2..|..1......2......1

.3..|..1....273 ...273......1

.4..|..1.....68...9282.....68......1

.5..|..1.....55...1870...1870.....55......1

.6..|..1....546..15015...3740..15015....546....1

.7..|..1.....29...7917...1595...1595...7917...29.....1

.8..|

CROSSREFS

Cf. A175669, A053657, A202339, A202367, A202368, A202369, A202917, A202941, A203484.

Sequence in context: A159767 A169658 A330199 * A164810 A322392 A089538

Adjacent sequences:  A178470 A178471 A178472 * A178474 A178475 A178476

KEYWORD

nonn,tabl

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Jan 02 2012

STATUS

approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)