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A050983
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de Bruijn's S(4,n).
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3
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1, 14, 786, 61340, 5562130, 549676764, 57440496036, 6242164112184, 698300344311570, 79881547652046140, 9301427008157320036, 1098786921802152516024, 131361675994216221116836
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is divisible by (n+1). Prime p divides a(p-1). Prime p>2 divides all a(n) from a((p+1)/2) to a(p-1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
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REFERENCES
| N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland Publishing Co., 1958. See chapters 4 and 6.
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LINKS
| Eric Weisstein's World of Mathematics, Binomial Sums
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FORMULA
| a(n)=sum(k=-n, +n, (-1)^k*binomial(2*n, n+k)^4) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 02 2005
a(n) = (-1)^n * HypergeometricPFQ[ {-2n, -2n, -2n, -2n}, {1, 1, 1}, -1]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
E.g.f.: Sum(n>=0,I^n*x^n/n!^4) * Sum(n>=0,(-I)^n*x^n/n!^4) = Sum(n>=0,a(n)*x^(2*n)/n!^4) where I^2=-1. [From Paul D. Hanna, Dec 21 2011]
a(n) ~ 0.125 k^(8n+3)/(Pi*n)^(3/2) where k = 2 cos(Pi/8) = A179260. This formula is due to de Bruijn 1958. [Charles R Greathouse IV, Dec 28 2011]
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MATHEMATICA
| Sum[ (-1)^(k+n)Binomial[ 2n, k ]^4, {k, 0, 2n} ]
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PROG
| (PARI) a(n)=sum(k=0, 2*n, (-1)^(k+n)*binomial(2*n, k)^4) \\ Charles R Greathouse IV, Dec 28 2011
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CROSSREFS
| Cf. A000984, A006480, A050984.
Sequence in context: A103426 A203750 A042519 * A183576 A002429 A064345
Adjacent sequences: A050980 A050981 A050982 * A050984 A050985 A050986
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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