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 A090367 Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution cube of this sequence. 3
 1, 1, 5, 34, 276, 2509, 24739, 259815, 2873376, 33207790, 398897289, 4960652325, 63676368387, 841741913795, 11438028248093, 159536511439266, 2281321298635427, 33411684617642665, 500761214428795093, 7674842860939188928, 120209960716130232745 (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))^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

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)