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A009454 E.g.f. sin(log(1+x)). 8
0, 1, -1, 1, 0, -10, 90, -730, 6160, -55900, 549900, -5864300, 67610400, -839594600, 11186357000, -159300557000, 2416003824000, -38894192662000, 662595375078000, -11911522255750000, 225382826562400000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = sum{k=0..n-1, (-1)^k*T(n-1, k)*cos(Pi*(n-k-1)/2)}; T(n, k)=abs(A008276(n, k)). - Paul Barry, Apr 18 2005

abs(a(n)) = abs(Re(product((k+I), k=1..(n-1)))) with I^2=-1. Example: abs(a(9))=55900 and product((k+I), k=1..(9-1)) = - 55900 + 46800 I => abs(part real of "product((k+I), k=1..(9-1))") = 55900. - Yalcin Aktar, Jul 02 2005

a(n+2) = -(2n+1)*a(n+1)-(n^2+1)*a(n), a(0)=0, a(1)=1. E.g. a(8)=6160 and -13*a(7)-37*a(6)=6160 because a(7)=-730 and a(6)=90. - Remy Lachaud (pacifik31(AT)aol.com), Dec 25 2005

a(n) = sum_{k=0}^{n/2} stirling1(n,2k+1)*(-1)^k. - Vladimir Kruchinin, Aug 03 2010

MATHEMATICA

CoefficientList[Series[Sin[Log[1+x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

FullSimplify[Table[-((-1)^n*(Gamma[1 + I]*Gamma[-I + n] + Gamma[1 - I]*Gamma[I + n])*Sinh[Pi]) / (2*Pi), {n, 0, 20}]] (* Vaclav Kotesovec, Jan 24 2015 *)

Table[-(-1)^n Re[Pochhammer[1+I, n-1]], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 13 2016 *)

PROG

(Maxima(?)) sum(stirling1(n, 2*k+1)*(-1)^(k), k, 0, n/2) [From Vladimir Kruchinin, Aug 03 2010]

CROSSREFS

Cf. A242652, A231530.

Sequence in context: A159733 A265325 A038726 * A231530 A242652 A162756

Adjacent sequences:  A009451 A009452 A009453 * A009455 A009456 A009457

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

STATUS

approved

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Last modified December 8 02:07 EST 2016. Contains 278902 sequences.