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A112494 Sixth diagonal of the Stirling2 triangle A048993 and sixth column of triangle A008278. 3
1, 63, 966, 7770, 42525, 179487, 627396, 1899612, 5135130, 12662650, 28936908, 62022324, 125854638, 243577530, 452329200, 809944464, 1404142047, 2364885369, 3880739170, 6220194750, 9759104355, 15015551265, 22693687380, 33738295500, 49402080000, 71327958156 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

T. D. Noe, Table of n, a(n) for n = 6..1000

S. Butler, P. Karasik, A note on nested sums, J. Int. Seq. 13 (2010), 10.4.4, page 5.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = Stirling2(n+6, n) with Stirling2(n, m)=A048993(n, m). a(n)= A008278(n+5, 6).

a(n) = sum(A008517(5, m+1)*binomial(n+5-m, 2*5), m=0..4) from the o.g.f. See p. 257 eq. (6.43) of the R . L. Graham et al. book quoted in A008517.

O.g.f.: x*sum(A008517(5, m+1)*x^m, m=0..4)/(1-x)^11 with the fifth row [1, 52, 328, 444, 120] of the second-order Eulerian triangle A008517.

E.g.f. with offset n=-4: exp(x)*sum(A112493(5, m)*(x^(m+5))/(m+5)!, m=0..5) with the k=5 row [1, 57, 546, 1750, 2205, 945] of triangle A112493.

a(n) = sum(A112493(5, m)*binomial(n+4, 5+m), m=0..5) from the e.g.f. (coefficients from A112493(5, m) are [1, 57, 546, 1750, 2205, 945]).

With an offset of 1 the o.g.f. is D^5(x/(1-x)), where D is the operator x/(1-x)*d/dx. - Peter Bala, Jul 02 2012

G.f.: x^6*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4) / (1 - x)^11. - Colin Barker, Nov 04 2017

MATHEMATICA

Table[StirlingS2[n, n-5], {n, 6, 100}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)

PROG

(Sage) [stirling_number2(n, n-5) for n in xrange(6, 30)] # Zerinvary Lajos, May 16 2009

(PARI) for(n=6, 50, print1(stirling(n, n-5, 2), ", ")) \\ G. C. Greubel, Oct 22 2017

(PARI) Vec(x^6*(1 + 52*x + 328*x^2 + 444*x^3 + 120*x^4) / (1 - x)^11 + O(x^40)) \\ Colin Barker, Nov 04 2017

CROSSREFS

Cf. A008517, A112493.

Cf. A001298 (fifth diagonal, resp. column).

Sequence in context: A201886 A232794 A091027 * A258004 A258014 A183076

Adjacent sequences:  A112491 A112492 A112493 * A112495 A112496 A112497

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 14 2005

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)