A306095 Number of plane partitions of n where parts are colored in (at most) 5 colors.

1, 5, 55, 430, 3605, 25980, 203280, 1417530, 10373080, 71595830, 501688880, 3376856755, 23181027055, 153326091805, 1024829902855, 6713038952355, 44092634675905, 284723995000530, 1845944380173205, 11791816763005330, 75485171060740630, 478105767714603130

Offset: 0

Author

M. F. Hasler, Sep 22 2018

Keywords

• nonn

Comments

a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among five given colors, since there is no term at all.

Examples

			For n = 1, there is only the partition [1], which can be colored in any of the five colors, whence a(1) = 5.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 5 + 25 + 25 = 55 distinct possibilities.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A091298, A208447.

Column 5 of A306100 and A306101. See A306099, A306093, A306094, A306096 for columns 2, 3, 4 and 6.

Programs

PARI

a(n)=!n+sum(k=1,n,A091298(n,k)*5^k)

Formula

a(n) = Sum_{k=1..n} A091298(n,k)*5^k.