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A002429
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Numerators of double sums of reciprocals.
(Formerly M4956 N2124)
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1
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1, 1, 14, 818, 141, 13063, 16774564, 1057052, 4651811, 778001383, 1947352646, 1073136102266, 72379420806883, 112229882767, 120372921248744, 13224581478608216, 2077531074698521033, 517938126297258811, 13785854249175914469406, 343586489824688536178, 1958290344469311726833
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also, numerators of coefficients of expansion of arctan(x)^3. - Ruperto Corso, Dec 09 2011
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REFERENCES
| A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 117.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 316.
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FORMULA
| a(n) is the numerator of 3*sum_{i=3..2*n+3} 2^(i-2)*binomial(2*(n+1),i-1)*stirling1(i,3)/ i!. - Ruperto Corso, Dec 09 2011
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MAPLE
| p2x:=proc(n) option remember: if(n=1) then RETURN(1) else RETURN(((n-1)*p2x(n-1)+1/(2*n-1))/n) fi: end proc;
p3x:=proc(n) option remember: if(n=1) then RETURN(1) else RETURN(((2*n-1)*p3x(n-1)+3*p2x(n))/(2*n+1)) fi: end proc;
A002429 := proc(n)
numer(p3x(n)) ;
end proc:
seq(A002429(n), n=1..25) ; # Ruperto Corso, Dec 09 2011
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PROG
| (PARI) stirling1(n, k)=if(n<1, 0, n!*polcoeff(binomial(x, n), k))
for(n=0, 25, print1(numerator(3/4*sum(i=3, 2*n+3, 2^i*binomial(2*(n+1), i-1)*stirling1(i, 3)/ i!))", ")) /* Ruperto Corso, Dec 09 2011 */
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CROSSREFS
| Cf. A008309, A049218.
Sequence in context: A042519 A050983 A183576 * A064345 A159871 A115458
Adjacent sequences: A002426 A002427 A002428 * A002430 A002431 A002432
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Ruperto Corso, Dec 09 2011
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