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

0,2

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.

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A091298, A208447.

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

Sequence in context: A015266 A138163 A335355 * A081300 A190543 A144894

Adjacent sequences: A306092 A306093 A306094 * A306096 A306097 A306098

Keyword

nonn

Author

M. F. Hasler, Sep 22 2018

Status

approved