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A053567 Stirling numbers of first kind, s(n+5, n). 8
-120, 1764, -13132, 67284, -269325, 902055, -2637558, 6926634, -16669653, 37312275, -78558480, 156952432, -299650806, 549789282, -973941900, 1672280820, -2792167686, 4546047198, -7234669596, 11276842500, -17247104875, 25922927745, -38343278610, 55880640270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 833.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

G. C. Greubel, A Note on Jain basis functions, arXiv:1612.09385 [math.CA], 2016.

FORMULA

a(n) = (-1)^n*binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2 + 23*n + 38)/8.

G.f.: x*(120 + 444*x + 328*x^2 + 52*x^3 + x^4)/(1-x)^11. See row k=4 of triangle A112007 for the coefficients.

E.g.f. with offset 5: exp(x)*(Sum_{m=0..5} A112486(5, m)*(x^(5+m)/(5+m)!).

a(n) = binomial(n+5, 6)*binomial(n+5, 2)*(3*n^2 + 23*n + 38)/8. From the g.f.

a(n) = (f(n+4, 5)/10!)*Sum_{m=0..min(5, n-1)} A112486(5, m)*f(10, 5-m)*f(n-1, m)), with the falling factorials f(n, m):=n*(n-1)*, ..., *(n-(m-1)). From the e.g.f.

MAPLE

A053567 := proc(n) (-1)^(n+1)*combinat[stirling1](n+5, n) ; end proc: # R. J. Mathar, Jun 08 2011

MATHEMATICA

Table[StirlingS1[n+5, n](-1)^(n-1), {n, 30}] (* Harvey P. Dale, Sep 21 2011 *)

PROG

(Sage) [stirling_number1(n, n-5)*(-1)^(n+1) for n in xrange(6, 26)] # Zerinvary Lajos, May 16 2009

(MAGMA) [(-1)^n*Binomial(n+5, 6)*Binomial(n+5, 2)*(3*n^2+23*n+38)/8: n in [1..30]]; // Vincenzo Librandi, Jun 09 2011

(PARI) a(n) = (-1)^(n-1)*stirling(n+5, n, 1); \\ Michel Marcus, Aug 29 2017

CROSSREFS

Next |Stirling1| diagonal A112002, 5th diagonal of A130534.

Sequence in context: A027795 A223427 A282899 * A056270 A001118 A052767

Adjacent sequences:  A053564 A053565 A053566 * A053568 A053569 A053570

KEYWORD

easy,sign

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000

EXTENSIONS

Definition edited by Eric M. Schmidt, Aug 29 2017

STATUS

approved

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Last modified February 20 19:06 EST 2018. Contains 299382 sequences. (Running on oeis4.)