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A016036
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Row sums of triangle A000369.
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6
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1, 4, 31, 361, 5626, 109951, 2585269, 71066626, 2236441141, 79289379361, 3127129674736, 135802922499949, 6439320471558781, 331026965612789356, 18338413238239145731, 1089132347371148170381, 69033182553940825258594
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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
| E.g.f. exp(1-(1-4*x)^(1/4))-1.
Recursion: a(n)= 6*(2*n-5)*a(n-1)-3*(16*n^2-96*n+145)*a(n-2)+2*(4*n-15)*(2*n-7)*(4*n-13)*a(n-3)+a(n-4), n >= 4; a(0) := 1, a(1)=1, a(2)=4, a(3)=31.
a(n)=((n-1)!*sum(m=1..n-1, (sum(k=1..n-m, binomial(n+k-1,n-1)*sum(j=0..k, binomial(j,n-m-3*k+2*j)*binomial(k,j)*3^(-n+m+3*k-j)*2^(n-m-5*k+3*j)*(-1)^(n-m-k))))/(m-1)!))+1; [From Vladimir Kruchinin, Oct 18 2011]
a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator 1/(1-x)^3*d/dx. Cf. A001515, A015735 and A028575. - Peter Bala, Nov 25 2011
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PROG
| (Maxima)
a(n):=((n-1)!*sum((sum(binomial(n+k-1, n-1)*sum(binomial(j, n-m-3*k+2*j)*binomial(k, j)*3^(-n+m+3*k-j)*2^(n-m-5*k+3*j)*(-1)^(n-m-k), j, 0, k), k, 1, n-m))/(m-1)!, m, 1, n-1))+1; [From Vladimir Kruchinin, Oct 18 2011]
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CROSSREFS
| Cf. A001515, A015735.
Sequence in context: A145561 A201628 A086677 * A000314 A128709 A138860
Adjacent sequences: A016033 A016034 A016035 * A016037 A016038 A016039
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KEYWORD
| nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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