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A209306 Binomial self convolution of sequence k-> A209305(k+1). 3
1, 6, 52, 608, 9000, 161320, 3395384, 82067848, 2239857464, 68123898696, 2284557569272, 83741888125064, 3330861429420984, 142875672420718024, 6574169480181294200, 322998830024467434760, 16876498518902786900792, 934400728689236533139016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..375

FORMULA

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

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

MATHEMATICA

(* Generating series *)

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

CoefficientList[Series[A'[x]^2, {x, 0, 20}], x] Table[n!, {n, 0, 20}]

(* Recurrences *)

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

a[1] = 1;

a[0] = 1;

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

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

CROSSREFS

Cf. A209305.

Sequence in context: A217486 A144345 A294158 * A271802 A097820 A166889

Adjacent sequences:  A209303 A209304 A209305 * A209307 A209308 A209309

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Jan 18 2013

STATUS

approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)