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Search: id:A075856
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| A075856 |
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Triangle formed from coefficients of the polynomials p[1]=x, p[n+1] := (n+x*(n+1))*p[n]+x*x*diff(p[n],x) |
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+0
2
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| 1, 1, 3, 2, 10, 15, 6, 40, 105, 105, 24, 196, 700, 1260, 945, 120, 1148, 5068, 12600, 17325, 10395, 720, 7848, 40740, 126280, 242550, 270270, 135135, 5040, 61416, 363660, 1332100, 3213210, 5045040, 4729725, 2027025
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Constant terms of polynomials related to Ramanujan psi polynomials (see Zeng reference).
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REFERENCES
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B. Drake, I. M. Gessel and G. Xin, Three proofs and a generalization of the Goulden-Litsyn-Shevelev conjecture ..., J. Integer Sequences, Vol. 10 (2007), #07.3.7.
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LINKS
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S. Ramanujan, Notebook entry
J. Zeng, A Ramanujan sequence that refines the Cayley formula for trees, Ramanujan J., 3(1999) 1, 45-54.
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EXAMPLE
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1; 1,3; 2,10,15; 6,40,105,105; etc
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CROSSREFS
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The left column is (n-1)! (A000142) and the right column is the double factorial numbers A001147. The sum of each line is n^n (A000312)
Cf. A001147, A000312, A000142.
Cf. A054589.
Sequence in context: A095675 A006743 A091811 this_sequence A025520 A099946 A011953
Adjacent sequences: A075853 A075854 A075855 this_sequence A075857 A075858 A075859
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KEYWORD
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nonn,tabl
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AUTHOR
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Frederic Chapoton (chapoton(AT)math.uqam.ca), Oct 15 2002
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