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A000597 Central factorial numbers.
(Formerly M5255 N2287)
1
36, 820, 7645, 44473, 191620, 669188, 1999370, 5293970, 12728936, 28285400, 58856655, 115842675, 217378200, 391367064, 679524340, 1142659012 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

REFERENCES

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

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=4..19.

Mircea Merca, A Special Case of the Generalized Girard-Waring Formula J. Integer Sequences, Vol. 15 (2012), Article 12.5.7.

Index entries for sequences related to factorial numbers

FORMULA

E.g.f.: x^4 * (x^5 + 75*x^4 + 603*x^3 + 1065*x^2 + 460*x + 36) / (1-x)^10.

a(n) = s(n,n-3)^2-2*s(n,n-4)*s(n,n-2)+2*s(n,n-5)*s(n,n-1)+2*s(n,n-6), where s(n,k) are Stirling numbers of the first kind, A048994. - Mircea Merca, Apr 03 2012

Recurrence: (n-4)*(2*n-7)*(35*n^2 - 49*n + 18)*a(n) = n^2*(2*n-1)*(35*n^2 + 21*n + 4)*a(n-1). - Vaclav Kotesovec, Feb 23 2015

For n>=4, a(n) = (2*n-5)*(2*n-3)*(2*n-1)*(35*n^2+21*n+4) * n! / 45360. - Vaclav Kotesovec, Feb 23 2015

MAPLE

1/(-1+z)^10*(z^5+75*z^4+603*z^3+1065*z^2+460*z+36);

seq(stirling1(n, n-3)^2-2*stirling1(n, n-4)*stirling1(n, n-2)+2*stirling1(n, n-5)*stirling1(n, n-1)+2*stirling1(n, n-6), n=0..30) [From Mircea Merca, Apr 03 2012]

MATHEMATICA

CoefficientList[Series[(x^5 + 75*x^4 + 603*x^3 + 1065*x^2 + 460*x + 36)/(1-x)^10, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 23 2015 *)

Table[(2*n-5)*(2*n-3)*(2*n-1)*(35*n^2+21*n+4)*n!/45360, {n, 4, 20}] (* Vaclav Kotesovec, Feb 23 2015 *)

CROSSREFS

Column 3 of triangle A008955.

Sequence in context: A028222 A028216 A028221 * A028214 A028197 A028209

Adjacent sequences:  A000594 A000595 A000596 * A000598 A000599 A000600

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 6 06:58 EST 2016. Contains 278775 sequences.