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A036074 E.g.f.: exp((exp(p*x) - p - 1)/p + exp(x)) for p=4. 8
1, 2, 9, 55, 412, 3619, 36333, 408888, 5080907, 68914023, 1011165446, 15935379409, 268125052373, 4792458452162, 90605469012877, 1805135197261131, 37775862401203916, 827992670793489263 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.

T. S. Motzkin, Sorting numbers ...: for a link to an annotated scanned version of this paper see A000262.

LINKS

Table of n, a(n) for n=0..17.

Index entries for sequences related to sorting

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565

FORMULA

a(n) = sum(sum(binomial(m,i)*sum(binomial(i,j)*(1/4)^j*(3*j+i)^n,j,0,i)*(-5/4)^(m-i),i,0,m)/m!,m,1,n), n > 0. - Vladimir Kruchinin, Sep 14 2010

MATHEMATICA

mx = 16; p = 4; Range[0, mx]! CoefficientList[ Series[ Exp[ (Exp[p*x] - p - 1)/p + Exp[x]], {x, 0, mx}], x] (* Robert G. Wilson v, Dec 12 2012 *)

PROG

(Maxima) a(n):=sum(sum(binomial(m, i)*sum(binomial(i, j)*(1/4)^j*(3*j+i)^n, j, 0, i)*(-5/4)^(m-i), i, 0, m)/m!, m, 1, n); /* Vladimir Kruchinin, Sep 14 2010 */

CROSSREFS

Cf. A001861, A002872, A002873, A002874, A002875, A036076, ...

Sequence in context: A001757 A267225 A078455 * A231172 A009363 A069564

Adjacent sequences:  A036071 A036072 A036073 * A036075 A036076 A036077

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by N. J. A. Sloane, Jul 11 2008 at the suggestion of Franklin T. Adams-Watters

STATUS

approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)