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Search: id:A002544
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| A002544 |
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a(n)=binomial(2*n+1,n)*(n+1)^2.
(Formerly M4855 N2075)
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+0
6
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| 1, 12, 90, 560, 3150, 16632, 84084, 411840, 1969110, 9237800, 42678636, 194699232, 878850700, 3931426800, 17450721000, 76938289920, 337206098790, 1470171918600, 6379820115900, 27569305764000, 118685861314020
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Coefficients for numerical differentiation.
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REFERENCES
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C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 514.
H. E. Salzer, Coefficients for numerical differentiation with central differences, J. Math. Phys., 22 (1943), 115-135.
J. Ser, Les Calculs Formels des S\'{e}ries de Factorielles. Gauthier-Villars, Paris, 1933, p. 92.
T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 21.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
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G.f.: (1 + 2x)/(1 - 4x)^5/2.
a(n-1)=sum(i1+i2+...+in) where the sum is over 0<=i1<=i2<=...<=in<=n. a(n)=(n+1)^2 C(2n+1, n) G.f.: (1 + 2x)/(1 - 4x)^(5/2). - David Callan (callan(AT)stat.wisc.edu), Nov 20 2003
(n^2)*(binomial(2*n,n))/2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2006
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MAPLE
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[seq ((n^2)*(binomial(2*n, n))/2, n=1..29)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2006
a:=n->sum(sum(binomial(2*n, n)/2, j=1..n), k=1..n): seq(a(n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007
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PROGRAM
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(PARI) a(n)=binomial(2*n+1, n)*(n+1)^2
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CROSSREFS
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Cf. A085373.
Equals A002736/2
Adjacent sequences: A002541 A002542 A002543 this_sequence A002545 A002546 A002547
Sequence in context: A022640 A090749 A130592 this_sequence A093801 A135173 A114860
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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