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A000457 Exponential generating function: (1+3x)/(1-2x)^(7/2).
(Formerly M4736 N2028)
12
1, 10, 105, 1260, 17325, 270270, 4729725, 91891800, 1964187225, 45831035250, 1159525191825, 31623414322500, 924984868933125, 28887988983603750, 959493919812553125, 33774185977401870000, 1255977541034632040625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.

F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 296.

H. W. Gould, Harris Kwong, Jocelyn Quaintance, On Certain Sums of Stirling Numbers with Binomial Coefficients, J. Integer Sequences, 18 (2015), #15.9.6.

C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.

C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.

Alexander Kreinin, Integer Sequences and Laplace Continued Fraction, Preprint 2016; https://www.researchgate.net/profile/Alexander_Kreinin/publication/294260037_Integer_Sequences_and_Laplace_Continued_Fraction/links/56bf5f5308ae2f498ef7effa.pdf

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Stirling Number of the First Kind.

FORMULA

(2n+3)!/ [3!*n!*2^n ].

a(n)=(n+1)*(2*n+3)!!/3, n>=0, with (2*n+3)!! = A001147(n+2).

CROSSREFS

Equals (1/2)*A000906.

Third column of triangle A001497.

Second column (m=1) of unsigned Laguerre-Sonin a=1/2 triangle |A130757|.

Contribution from Johannes W. Meijer, May 24 2009: (Start)

Cf. A160473.

(End)

Contribution from Johannes W. Meijer, Oct 16 2009: (Start)

Equals row sums of A163939.

(End)

Sequence in context: A123512 A079515 A024131 * A240681 A113348 A193274

Adjacent sequences:  A000454 A000455 A000456 * A000458 A000459 A000460

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sascha Kurz, Aug 15 2002

STATUS

approved

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Last modified August 18 12:18 EDT 2017. Contains 290720 sequences.