A006543 Maximal iterated binomial coefficients.

1, 2, 3, 4, 5, 6, 10, 15, 45, 120, 990, 14190, 489555, 161226780, 476106503180, 19554673086218985, 698490144518203427450060, 17987097565293886931115539020016860, 1246236391932004987381133823926620650891666994820

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• C. L. Mallows, Letter to N. J. A. Sloane, 1980.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..27
• Solomon W. Golomb, Iterated binomial coefficients, Amer. Math. Monthly, 87 (1980), 719-727.
• C. L. Mallows, Letter to N. J. A. Sloane, 1980

Formula

a(n) = max{(a_1; a_2; ...; a_k)} where a_1,a_2,...,a_k runs over all the compositions of n and (a_1)=a_1, (a_1; a_2) = binomial(a_1, a_2), and (a_1; a_2; ...; a_(k-1); a_k) = ((a_1; a_2; ..., a_(k-1)); a_k). - Sean A. Irvine, May 07 2017

Extensions

More terms from Sean A. Irvine, May 07 2017