Search: id:A001514
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%I A001514 M4654 N1993
%S A001514 0,1,9,81,835,9990,137466,2148139,37662381,733015845,15693217705,
%T A001514 366695853876,9289111077324,253623142901401,7425873460633005,232122372003909045,
%U A001514 7715943399320562331,271796943164015920914,10114041937573463433966
%N A001514 Bessel polynomial {y_n}'(1).
%D A001514 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001514 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001514 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A001514 <a href="Sindx_Be.html#Bessel">Index entries for sequences related to 
               Bessel functions or polynomials</a>
%F A001514 (1/2) * Sum((n+k+2)!/((n-k)!*k!*2^k),k=0..n) (with a different offset).
%p A001514 (As in A001497 define:) f := proc(n) option remember; if n <=1 then (1+x)^n 
               else expand((2*n-1)*x*f(n-1)+f(n-2)); fi; end;
%p A001514 [seq( subs(x=1,diff(f(n),x)),n=0..60)];
%p A001514 f2:=proc(n) local k; add((n+k+2)!/((n-k)!*k!*2^k),k=0..n); end; [seq(f2(n),
               n=0..60)]; # uses a different offset
%Y A001514 Cf. A001515, A001516, A001518, A065920, A144505.
%Y A001514 Sequence in context: A101601 A144821 A137062 this_sequence A077364 A067478 
               A077486
%Y A001514 Adjacent sequences: A001511 A001512 A001513 this_sequence A001515 A001516 
               A001517
%K A001514 nonn
%O A001514 0,3
%A A001514 N. J. A. Sloane (njas(AT)research.att.com).

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