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A025749
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4th order Patalan numbers (generalization of Catalan numbers).
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5
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1, 1, 6, 56, 616, 7392, 93632, 1230592, 16612992, 228890112, 3204461568, 45445091328, 651379642368, 9419951751168, 137262154088448, 2013178259963904, 29694379334467584, 440175505428578304
(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.: (5-(1-16*x)^(1/4))/4. a(n) = 4^(n-1)*3*A034176(n-1)/n!, n >= 2; 3*A034176(n-1)=(4*n-5)(!^4) := product(4*j-5, j=2..n) - from wolfdieter.lang(AT)physik.uni-karlsruhe.de.
a(n):=(4^(n-1)*sum(k=1..n-1, binomial(n+k-1,n-1)*sum(j=0..k, binomial(j,n-3*k+2*j-1)*4^(j-k)*binomial(k,j)*3^(-n+3*k-j+1)*2^(n-3*k+j-1)*(-1)^(n-3*k+2*j-1))))/n; [Vladimir Kruchinin kru(AT)ie.tusur.ru Apr 01 2011]
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PROG
| (Maxima)
a(n):=(4^(n-1)*sum(binomial(n+k-1, n-1)*sum(binomial(j, n-3*k+2*j-1)*4^(j-k)*binomial(k, j)*3^(-n+3*k-j+1)*2^(n-3*k+j-1)*(-1)^(n-3*k+2*j-1), j, 0, k), k, 1, n-1))/n; [Vladimir Kruchinin kru(AT)ie.tusur.ru Apr 01 2011]
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CROSSREFS
| Equals 2^n * A048779(n), n>0.
Sequence in context: A099140 A048348 A199755 * A182955 A053336 A112699
Adjacent sequences: A025746 A025747 A025748 * A025750 A025751 A025752
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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