A238632 - OEIS

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A238632

Number of partitions of 5^n into parts that are at most 5.

1, 7, 377, 106852, 55567352, 33432635477, 20735819929227, 12940003469288602, 8085018247233663602, 5052825953808096554227, 3157977415776418319210477, 1973731034215692844676632352, 1233581290054852867292137569852, 770988230493054044846859764522977

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..350

FORMULA

a(n) = [x^(5^n)] Product_{j=1..5} 1/(1-x^j).

G.f.: (1953125*x^5+4828125*x^4-2015125*x^3+96440*x^2-774*x+1) / Product_{j=0..4} 1-5^j*x.

MAPLE

gf:= (1953125*x^5+4828125*x^4-2015125*x^3+96440*x^2-774*x+1)/mul(1-5^j*x, j=0..4):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..20);