A090366 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution of this sequence.

1, 1, 4, 21, 131, 917, 6988, 56965, 491240, 4447558, 42048457, 413473928, 4215959294, 44469487070, 484303175837, 5437300482651, 62848069403649, 747063566345320, 9123406697372938, 114370704441951620, 1470590692488141315, 19381056189738194070

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))^2*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:
b:= invtr(bintr(n-> add(a(i)*a(n-i), i=0..n))):
a:= n-> `if`(n<0, 0, b(n-1)):
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 28 2012

Mathematica

m = 30; A[_] = 1; Do[A[x_] = 1/(1 - A[x/(1-x)]^2*(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^2, x, x/(1-x))/(1-x)+x*O(x^n); A=1+x*A*B); polcoeff(A, n, x)))}

Crossrefs

Cf. A090365, A090367.

Sequence in context: A141052 A058308 A078591 * A273956 A131965 A332851

Adjacent sequences: A090363 A090364 A090365 * A090367 A090368 A090369

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2003

Status

approved