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Search: id:A000373
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| A000373 |
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Conjectured dimension of a module associated with the free commutative Moufang loop with n generators. |
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+0
2
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| 0, 0, 1, 8, 44, 214, 1000, 4592, 20888, 94846, 434973, 2042836, 9979086, 51460622, 283839957, 1688139424, 10859199656, 75338888918, 560740210491, 4445766353604, 37329808482989, 330143634313064, 3064464030121369
(list; graph; listen)
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OFFSET
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1,4
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REFERENCES
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Yu. I. Manin, Cubic Forms, Second edition, North-Holland Publishing Co., Amsterdam, 1986, page 312. MR0833513 (87d:11037)
Smith, Jonathan D. H.; Commutative Moufang loops and Bessel functions. Invent. Math. 67 (1982), no. 1, 173-187.
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PROGRAM
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(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 */
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CROSSREFS
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Sequence in context: A100575 A003220 A125318 this_sequence A082762 A147828 A155604
Adjacent sequences: A000370 A000371 A000372 this_sequence A000374 A000375 A000376
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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