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A025750
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5th order Patalan numbers (generalization of Catalan numbers).
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3
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1, 1, 10, 150, 2625, 49875, 997500, 20662500, 439078125, 9513359375, 209293906250, 4661546093750, 104884787109375, 2380077861328125, 54401779687500000, 1251240932812500000, 28934946571289062500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| G.f.: (6-(1-25*x)^(1/5))/5.
a(n) = 5^(n-1)*4*A034301(n-1)/n!, n >= 2; 4*A034301(n-1)= (5*n-6)(!^5) := product(5*j-6, j=2..n) - from wolfdieter.lang(AT)physik.uni-karlsruhe.de
a(n)=(sum(k=0..n-1, (-1)^(n-k-1)*binomial(n+k-1,n-1)*sum(j=0..k, 2^j*binomial(k,j)*sum(i=j..n-k+j-1, binomial(j,i-j)*binomial(k-j,n-3*(k-j)-i-1)*5^(3*(k-j)+i)))))/n, n>0, a(0)=1. [From Vladimir Kruchinin, Dec 10 2011]
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PROG
| (Maxima)
a(n):=if n=0 then 1 else (sum((-1)^(n-k-1)*binomial(n+k-1, n-1)*sum(2^j*binomial(k, j)*sum(binomial(j, i-j)*binomial(k-j, n-3*(k-j)-i-1)*5^(3*(k-j)+i), i, j, n-k+j-1), j, 0, k), k, 0, n-1))/(n); [From Vladimir Kruchinin, Dec 10 2011]
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CROSSREFS
| Cf. A034687, A049393.
Sequence in context: A098270 A157867 A116156 * A034325 A178298 A048907
Adjacent sequences: A025747 A025748 A025749 * A025751 A025752 A025753
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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