A203646 Number of arrays of n 0..15 integers with new values introduced in order 0..15 but otherwise unconstrained.

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869803, 682076806005, 5832742192288, 51724157478221, 474869780161021, 4506714279517080, 44151953491540255

Offset: 1

Author

R. H. Hardin, Jan 04 2012

Keywords

• nonn

Comments

Column 15 of A203647.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (121, -6685, 223405, -5042947, 81308227, -965408015, 8576039615, -57312583328, 287212533608, -1066335473840, 2866534951280, -5367984964224, 6557974412544, -4622628648960, 1394852659200).

Crossrefs

Cf. A203641.

Formula

Empirical: a(n) = 121*a(n-1) -6685*a(n-2) +223405*a(n-3) -5042947*a(n-4) [phone]*a(n-5) -965408015*a(n-6) [phone]*a(n-7) -57312583328*a(n-8) [phone]*a(n-9) -1066335473840*a(n-10) [phone]*a(n-11) -5367984964224*a(n-12) [phone]*a(n-13) -4622628648960*a(n-14) [phone]*a(n-15).

Empirical formula confirmed by extension of first ten columns, see A203641. - Ray Chandler, Jul 06 2024