A107092 G.f. A(x) satisfies A(x)^3 = A(x^3) + 3*x.

1, 1, -1, 2, -4, 9, -22, 55, -142, 376, -1011, 2758, -7614, 21220, -59630, 168759, -480533, 1375676, -3957075, 11430582, -33144264, 96434321, -281447954, 823734157, -2417092933, 7109265120, -20955593252, 61893804180, -183148075432, 542885589115, -1611809502764, 4792612539375

Offset

0,4

Comments

Self-convolution cube is A107093.

Links

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

Ira M. Gessel, The Amdeberhan-Konvalinka Conjecture and Symmetric Functions, Séminaire Lotharingien Comb. (2024). See p. 83 of 109.

Example

A(x)^3 = 1 + 3*x + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18 +...
A(x^3) = 1 + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18+...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^3)+3*x+x*O(x^n))^(1/3)); polcoeff(A, n, x)}

Crossrefs

Cf. A107093, A008544, A352703, A352705, A361763.

Sequence in context: A198520 A115324 A196307 * A352702 A055588 A088456

Adjacent sequences: A107089 A107090 A107091 * A107093 A107094 A107095

Keyword

sign

Author

Paul D. Hanna, May 11 2005

Status

approved