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A100101 Bell(2n)*(2n-1)!!, where Bell are the Bell numbers A000110. 0
1, 2, 45, 3045, 434700, 109596375, 43800340815, 25797179878470, 21243510135522675, 23503974546075598575, 33865310276598741840900, 61964234361152712204340725, 141027420945032510510113517025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence arises in the normal ordering problem the exponential of square of boson number operator.

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) = Bell(2*n)*(2*n)!/(2^n*n!) = A001147(n)*A000110(2*n).

E.g.f.: G(x) = Sum_{k>=0} exp((k*x)^2/2-1)/k!; a(n) = subs(x=0, (d^(2n)/dx^(2n))G(x)).

MATHEMATICA

Array[BellB[2 #] (2 # - 1)!! &, 13, 0] (* Michael De Vlieger, Dec 24 2017 *)

PROG

(PARI) a(n)=round(exp(-1)*suminf(k=0, k^(2*n)/k!))*(2*n)!/(2^n*n!) \\ Charles R Greathouse IV, Nov 06 2011

CROSSREFS

Cf. A000110, A001147.

Sequence in context: A222997 A092654 A209606 * A332244 A090601 A266016

Adjacent sequences:  A100098 A100099 A100100 * A100102 A100103 A100104

KEYWORD

nonn

AUTHOR

Karol A. Penson, Nov 03 2004

STATUS

approved

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Last modified August 6 14:19 EDT 2020. Contains 336246 sequences. (Running on oeis4.)