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

Author

Paul D. Hanna, Nov 26 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A090365, A090367.

Programs

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 *)

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))}

Formula

G.f.: A(x) = 1/(1 - A(x/(1-x))^2*x/(1-x) ).