A369115 Expansion of (1 - x)^(-2) * Sum_{j>=0} (x^j / (1 - Sum_{k=1..j} x^k)).

1, 3, 7, 14, 26, 46, 80, 138, 239, 417, 735, 1309, 2355, 4275, 7823, 14416, 26728, 49820, 93300, 175454, 331170, 627154, 1191204, 2268604, 4330915, 8286101, 15884857, 30507175, 58686513, 113066033, 218137531, 421391695, 814999229, 1578000229, 3058458885, 5933549906

Offset: 0

Author

Peter Luschny, Jan 21 2024

Keywords

• nonn

Comments

Considering more generally the family of generating functions (1 - x)^n * Sum_{j>=0} (x^j / (1 - Sum_{k=1..j} x^k)) one finds several sequences related to compositions as indicated in the cross-references.

Crossrefs

Cf. This sequence (n=-2), A186537 left shifted (n=-1), A079500 (n=0), A368279 (n=1), A369116 (n=2).

Programs

Maple

gf := (1 - x)^(-2) * add(x^j / (1 - add(x^k, k = 1..j)), j = 0..42):
ser := series(gf, x, 40): seq(coeff(ser, x, k), k = 0..38);

Formula

Partial sums of A186537 starting at n = 1.