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 A209306 Binomial self convolution of sequence k-> A209305(k+1). 3

%I

%S 1,6,52,608,9000,161320,3395384,82067848,2239857464,68123898696,

%T 2284557569272,83741888125064,3330861429420984,142875672420718024,

%U 6574169480181294200,322998830024467434760,16876498518902786900792,934400728689236533139016

%N Binomial self convolution of sequence k-> A209305(k+1).

%H G. C. Greubel, <a href="/A209306/b209306.txt">Table of n, a(n) for n = 0..375</a>

%F b(n) = Sum_{k=0,..,n} C(n,k)*a(k+1)*a(n-k+1), where a(n) = A209305(n).

%F E.g.f.: B(x) = A'(x)^2, where A(x) is the e.g.f. of sequence A209305.

%t (* Generating series *)

%t A[x_] := InverseErf[(2 Exp[x] - 2 + Exp[1] Sqrt[Pi] Erf[1])/(Exp[1] Sqrt[Pi])];

%t CoefficientList[Series[A'[x]^2, {x, 0, 20}], x] Table[n!, {n, 0, 20}]

%t (* Recurrences *)

%t a[n_] := a[n] = a[n-1]+2Sum[Binomial[n-2,k]a[k]b[n-2-k],{k,0,n-2}];

%t a[1] = 1;

%t a[0] = 1;

%t b[n_] := Sum[Binomial[n,k]a[k+1]a[n-k+1],{k,0,n}];

%t Table[b[n], {n, 0, 100}]

%Y Cf. A209305.

%K nonn

%O 0,2

%A _Emanuele Munarini_, Jan 18 2013

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Last modified September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)