Search: id:A065919
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%I A065919
%S A065919 1,5,61,1225,34361,1238221,54516085,2836074641,170218994545,11577727703701,
%T A065919 880077524475821,73938089783672665,6803184337622361001,680392371852019772765,
%U A065919 73489179344355757819621,8525425196317119926848801,1057226213522667226687070945
%N A065919 Bessel polynomial y_n(4).
%D A065919 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A065919 Harry J. Smith, <a href="b065919.txt">Table of n, a(n) for n=0,...,100</
               a>
%H A065919 <a href="Sindx_Be.html#Bessel">Index entries for sequences related to 
               Bessel functions or polynomials</a>
%F A065919 y_n(x) = sum ((n+k)!*(x/2)^k/((n-k)!*k!), k=0..n);
%F A065919 Main diagonal of A143411. Recurrence relation: a(0) = 1, a(1) = 5, a(n) 
               = 4*(2*n-1)*a(n-1) + a(n-2) for n >= 2. Sequence A143412(n) satisfies 
               the same recurrence relation. 1/sqrt(e) = 1 - 2*sum {n = 0..inf} 
               (-1)^n/(a(n)*a(n+1)) = 1 - 2*(1/(1*5) - 1/(5*61) + 1/(61*1225) - 
               ...). [From Peter Bala (pbala(AT)toucansurf.com), Aug 14 2008]
%o A065919 (PARI) { for (n=0, 100, if (n>1, a=4*(2*n - 1)*a1 + a2; a2=a1; a1=a, 
               if (n, a=a1=5, a=a2=1)); write("b065919.txt", n, " ", a) ) } [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 04 2009]
%Y A065919 Cf. A001515, A001517, A001518.
%Y A065919 Polynomial coefficients are in A001498.
%Y A065919 A143411 (main diagonal), A143412. [From Peter Bala (pbala(AT)toucansurf.com), 
               Aug 14 2008]
%Y A065919 Sequence in context: A146760 A083082 A009825 this_sequence A096537 A115047 
               A028296
%Y A065919 Adjacent sequences: A065916 A065917 A065918 this_sequence A065920 A065921 
               A065922
%K A065919 nonn
%O A065919 0,2
%A A065919 N. J. A. Sloane (njas(AT)research.att.com), Dec 08 2001
%E A065919 Recurrence relation a(2) = 5 corrected to a(1) = 5 by Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Nov 04 2009

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