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A154372
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Triangle T(n,k) = (k+1)^(n-k)*binomial(n,k).
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2
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1, 1, 1, 1, 4, 1, 1, 12, 9, 1, 1, 32, 54, 16, 1, 1, 80, 270, 160, 25, 1, 1, 192, 1215, 1280, 375, 36, 1, 1, 448, 5103, 8960, 4375, 756, 49, 1, 1, 1024, 20412, 57344, 43750, 12096, 1372, 64, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| From A152650/A152656,coefficients of other exponential polynomials(*). a(n) is triangle A152818 where terms of each column is divided by the beginning one. See A000004, A001787(n+1), A006043=2*A027472, A006044=6*A038846.
(*) Not factorial as written in A006044. See A000110,Bell-Touchard. Second diagonal is 1,4,9,16,25, denominators of Lyman's spectrum of hydrogen,A000290(n+1)=deleted A147883,which has homogeneous indices for denominators series of Rydberg-Ritz spectrum of hydrogen.
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FORMULA
| T(n,k) = (k+1)^(n-k)*binomial(n,k). k!*T(n,k) gives the entries for A152818 read as a triangular array.
E.g.f.: exp(x*(1+t*exp(x))) = 1+(1+t)*x+(1+4*t+t^2)*x^2/2!+(1+12*t+9*t^2+t*3)*x^3/3!+.... O.g.f.: sum {k = 1..inf} (t*x)^(k-1)/(1-k*x)^k = 1+(1+t)*x+(1+4*t+t^2)*x^2+.... Row sums are A080108. - Peter Bala, Oct 09 2011
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CROSSREFS
| Cf. A080108, A152818.
Sequence in context: A205946 A101919 A055106 * A080416 A168619 A099759
Adjacent sequences: A154369 A154370 A154371 * A154373 A154374 A154375
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jan 08 2009
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