A352530 -id:A352530 - cp's OEIS frontend

A352529 Expansion of 1/Sum_{k>=0} x^(k^4).

1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -15, 14, -12, 9, -5, 0, 6, -13, 21, -30, 40, -51, 63, -76, 90, -105, 120, -134, 146, -155, 160, -160, 154, -141, 120, -90, 50, 1, -64, 140, -230, 335, -455, 589, -735, 890, -1050, 1210, -1364, 1505

Offset: 0

Seiichi Manyama, Mar 19 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000583, A317665, A323633, A352530.

my(N=99, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/4), x^k^4))

a(n) = if(n==0, 1, -sum(k=1, n, ispower(k, 4)*a(n-k)));

A363749 Number of compositions into sums of fifth powers.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 38, 42, 47, 53, 60, 68, 77, 87, 98, 110, 123, 137, 152, 168, 185

Offset: 0

Seiichi Manyama, Jun 19 2023

nonn

This sequence is different from A291168.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A006456, A023358, A363748.

Cf. A000584, A291168, A352530.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, ispower(j, 5)*v[i-j+1])); v;

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

cp's OEIS Frontend

A352529 Expansion of 1/Sum_{k>=0} x^(k^4).

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A363749 Number of compositions into sums of fifth powers.

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