A382372 Expansion of 1/( 1 - Sum_{k>=0} x^(4^k) / (1 - x^(4^k)) ).

1, 1, 2, 4, 9, 18, 37, 76, 158, 325, 670, 1381, 2850, 5876, 12117, 24986, 51530, 106262, 219131, 451885, 931876, 1921695, 3962884, 8172182, 16852538, 34752996, 71667001, 147790386, 304770689, 628492615, 1296066140, 2672724207, 5511643710, 11366012289

Offset: 0

Author

Seiichi Manyama, Mar 23 2025

Keywords

• nonn

Crossrefs

Cf. A327736, A382367, A382373, A382378.

Cf. A115362.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A115362(k-1) * a(n-k).

G.f.: 1/(1 - Sum_{i>=1, j>=0} x^(i*4^j)).

G.f. A(x) satisfies A(x) = 1/( 1/A(x^4) - x/(1-x) ).