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A090366 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution of this sequence. 3
1, 1, 4, 21, 131, 917, 6988, 56965, 491240, 4447558, 42048457, 413473928, 4215959294, 44469487070, 484303175837, 5437300482651, 62848069403649, 747063566345320, 9123406697372938, 114370704441951620, 1470590692488141315, 19381056189738194070 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)