A132330 -id:A132330 - cp's OEIS frontend

A132331 G.f.: A(x) = (A_1)^3 where A_1 = 1 + x(A_2)^3; A_2 = 1 + x^2(A_3)^3; A_3 = 1 + x^3(A_4)^3; ... A_n = 1 + x^n(A_{n+1})^3 for n>=1.

1, 3, 3, 10, 18, 18, 72, 93, 141, 381, 423, 990, 1701, 2304, 4998, 7275, 12960, 21195, 34812, 58860, 90576, 163603, 239445, 413964, 669096, 1017918, 1768608, 2639988, 4383036, 6880680, 10911267, 17411292, 26930250, 43797420, 66324909, 107180772

Offset: 0

Paul D. Hanna, Aug 20 2007

nonn

Cf. A132330 (cube-root); A001764; A095830 (variant).

{a(n)=local(A=1+x*O(x^n)); for(j=0,n-1,A=1+x^(n-j)*A^3);polcoeff(A^3,n)}

Self-convolution cube of A132330.

A302693 a(n) = [x^n] 1 + x(1 + x^2(1 + x^3(1 + x^4(1 + x^5*(1 + ...)^n)^n)^n)^n)^n.

Original entry on oeis.org

1, 1, 0, 3, 0, 10, 36, 35, 448, 450, 4600, 13167, 45408, 240006, 670124, 3863835, 13209088, 60533974, 268324056, 1089776654, 5328589520, 22065836226, 106289169448, 481033496803, 2231768294208, 10748702587800, 49858509230920, 245664498591891, 1175943617623264

Offset: 0

Ilya Gutkovskiy, Apr 11 2018

nonn

Cf. A010054, A108643, A132330, A302657, A302686.

Table[SeriesCoefficient[1 + x Fold[(x^(#2 + 1) #1 + 1)^n &, 0, Reverse[Range[n]]], {x, 0, n}], {n, 0, 28}]

cp's OEIS Frontend

A132331 G.f.: A(x) = (A_1)^3 where A_1 = 1 + x(A_2)^3; A_2 = 1 + x^2(A_3)^3; A_3 = 1 + x^3(A_4)^3; ... A_n = 1 + x^n(A_{n+1})^3 for n>=1.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A302693 a(n) = [x^n] 1 + x(1 + x^2(1 + x^3(1 + x^4(1 + x^5*(1 + ...)^n)^n)^n)^n)^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

cp's OEIS Frontend

A132331 G.f.: A(x) = (A_1)^3 where A_1 = 1 + x*(A_2)^3; A_2 = 1 + x^2*(A_3)^3; A_3 = 1 + x^3*(A_4)^3; ... A_n = 1 + x^n*(A_{n+1})^3 for n>=1.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A302693 a(n) = [x^n] 1 + x*(1 + x^2*(1 + x^3*(1 + x^4*(1 + x^5*(1 + ...)^n)^n)^n)^n)^n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A132331 G.f.: A(x) = (A_1)^3 where A_1 = 1 + x(A_2)^3; A_2 = 1 + x^2(A_3)^3; A_3 = 1 + x^3(A_4)^3; ... A_n = 1 + x^n(A_{n+1})^3 for n>=1.

A302693 a(n) = [x^n] 1 + x(1 + x^2(1 + x^3(1 + x^4(1 + x^5*(1 + ...)^n)^n)^n)^n)^n.