A372956 G.f. A(x) satisfies A(x)^5 = A(x^5) / (1 - 5*x)^5 with A(0)=1.

1, 5, 25, 125, 625, 3126, 15630, 78150, 390750, 1953750, 9768753, 48843765, 244218825, 1221094125, 6105470625, 30527353136, 152636765680, 763183828400, 3815919142000, 19079595710000, 95397978550044, 476989892750220, 2384949463751100, 11924747318755500, 59623736593777500

Offset

0,2

Comments

Euler transform of 5 * A054662(n).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

OEIS Wiki, Euler transform

Formula

G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A054662(k) )^5.

Example

A(x)^5 = 1 + 25*x + 375*x^2 + 4375*x^3 + 43750*x^4 + 393755*x^5 + ... .

Prog

(PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
my(N=30, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 5))^5)

Crossrefs

Cf. A372870, A372957.

Cf. A054662, A372535.

Sequence in context: A050735 A195948 A083590 * A361765 A370546 A097680

Adjacent sequences: A372953 A372954 A372955 * A372957 A372958 A372959

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2024

Status

approved