Search: id:A000373
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%I A000373
%S A000373 0,0,1,8,44,214,1000,4592,20888,94846,434973,2042836,9979086,51460622,
%T A000373 283839957,1688139424,10859199656,75338888918,560740210491,
%U A000373 4445766353604,37329808482989,330143634313064,3064464030121369
%N A000373 Conjectured dimension of a module associated with the free commutative 
               Moufang loop with n generators.
%D A000373 Yu. I. Manin, Cubic Forms, Second edition, North-Holland Publishing Co., 
               Amsterdam, 1986, page 312. MR0833513 (87d:11037)
%D A000373 Smith, Jonathan D. H.; Commutative Moufang loops and Bessel functions. 
               Invent. Math. 67 (1982), no. 1, 173-187.
%o A000373 (PARI) a(n)=local(A); if(n<3,0, A=Vec(-1+serlaplace(serlaplace(subst(1/
               besselj(0,x+O(x^n)),x^2,4*x)))); A[1]=0; sum(k=1,(n-1)\2,sum(p=0,
               n-2*k-1,n!/p!/(2*k+1)!/(n-p-2*k-1)!*(A[k]+binomial(p+k-1,k-1))))) 
               /* Michael Somos May 17 2004 */
%Y A000373 Sequence in context: A100575 A003220 A125318 this_sequence A082762 A147828 
               A155604
%Y A000373 Adjacent sequences: A000370 A000371 A000372 this_sequence A000374 A000375 
               A000376
%K A000373 nonn
%O A000373 1,4
%A A000373 N. J. A. Sloane (njas(AT)research.att.com).

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