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A004981
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(2^n/n!)*product[ k=0..n-1 ](4*k + 1).
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6
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1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, 7049900, 52169260, 388898120, 2916735900, 21987701400, 166478310600, 1265235160560, 9647418099270, 73774373700300, 565603531702300, 4346216612028200, 33465867912617140
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The convolution of this sequence with itself yields A059304. - T. D. Noe (noe(AT)sspectra.com), Jun 11 2002
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REFERENCES
| A. Vogt, Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation, Arxiv preprint arXiv:1108.2993, 2011
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FORMULA
| a(n) ~ Gamma(1/4)^-1*n^(-3/4)*2^(3*n)*{1 - 3/32*n^-1 - ...}
G.f.: (1-8x)^(-1/4).
A002897(n)=Sum_{k=0..n} a(k)^2*a(n-k)^2. - Michael Somos Jan 31 2007
a(n):=(sum(m=1..n, m*sum(k=m..n, binomial(-m+2*k-1,k-1)*2^(n+m-k)*binomial(2*n-k-1,n-1))))/(n), n>0, a(0)=1. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Dec 26 2011]
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PROG
| (PARI) a(n)=if(n<0, 0, prod(k=1, n, (8*k-6)/k))
{a(n)=if(n<0, 0, polcoeff( (1-8*x+x*O(x^n))^(-1/4), n))} /* Michael Somos Jan 31 2007 */
(Maxima) a(n):=if n=0 then 1 else (sum(m*sum(binomial(-m+2*k-1, k-1)*2^(n+m-k)*binomial(2*n-k-1, n-1), k, m, n), m, 1, n))/(n); /* From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Dec 26 2011 */
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CROSSREFS
| Sequence in context: A025188 A114620 A173613 * A137571 A098616 A082042
Adjacent sequences: A004978 A004979 A004980 * A004982 A004983 A004984
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 01 2000
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