A112494 Sixth diagonal of the Stirling2 triangle A048993 and sixth column of triangle A008278.

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

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, n-5) 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 range(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