A090367 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution cube of this sequence.

1, 1, 5, 34, 276, 2509, 24739, 259815, 2873376, 33207790, 398897289, 4960652325, 63676368387, 841741913795, 11438028248093, 159536511439266, 2281321298635427, 33411684617642665, 500761214428795093, 7674842860939188928, 120209960716130232745

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

G.f.: A(x) = 1/(1 - A(x/(1-x))^3*x/(1-x) ).

Maple

bintr:= proc(p) local b; b:= proc(n) option remember;
           add(p(k) *binomial(n, k), k=0..n) end
        end:
invtr:= proc(p) local b; b:= proc(n) option remember;
           `if`(n<1, 1, add(b(n-i) *p(i-1), i=1..n+1)) end
        end:
s:= proc(n) option remember; add(a(i)*a(n-i), i=0..n) end:
b:= invtr(bintr(n-> add(s(i)*a(n-i), i=0..n))):
a:= n-> `if`(n<0, 0, b(n-1)):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 28 2012

Mathematica

m = 25; A[_] = 1; Do[A[x_] = 1/(1 - A[x/(1-x)]^3*(x/(1-x))) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Jun 04 2018 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^3, x, x/(1-x))/(1-x)+x*O(x^n); A=1+x*A*B); polcoeff(A, n, x))}

Crossrefs

Cf. A090365, A090366.

Sequence in context: A116435 A292877 A257887 * A189488 A111557 A211794

Adjacent sequences: A090364 A090365 A090366 * A090368 A090369 A090370

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2003

Status

approved