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 A127548 O.g.f.: Sum_{n>=0} n!*(x/(1+x)^2)^n. 2
 1, 1, 0, 1, 4, 19, 112, 771, 6088, 54213, 537392, 5867925, 69975308, 904788263, 12607819040, 188341689287, 3002539594128, 50878366664393, 913161208490016, 17304836525709097, 345279674107957524, 7235298537356113339 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n+1) = inverse binomial transform of A013999 = Sum_{k=0..n)}binomial(n,k)*(-1)^(n-k)*A013999(k). - Emanuele Munarini, Jul 01 2013 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..450 FORMULA a(n) = Sum_{s=1..n} (-1)^(n-s)*s!*C(s+n-1,2s-1) if n>=1, where C(a,b)=binomial(a,b). - R. J. Mathar, Jul 13 2007 G.f.: Q(0) where Q(k) = 1 + (2*k + 1)*x/( (1+x)^2- 2*x*(1+x)^2*(k+1)/(2*x*(k+1) + (1+x)^2/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Mar 08 2013 a(n) = A000271(n) + A000271(n-1). - Peter Bala, Sep 02 2016 a(n) ~ exp(-2) * n!. - Vaclav Kotesovec, Oct 31 2017 MAPLE A127548 := proc(n) if n = 0 then 1 ; else add(factorial(s)*(-1)^(n-s)*binomial(s+n-1, 2*s-1), s=1..n) ; fi ; end: for n from 0 to 20 do printf("%d, ", A127548(n)) ; od ; # R. J. Mathar, Jul 13 2007 MATHEMATICA nn = 21; CoefficientList[Series[Sum[n!*(x/(1 + x)^2)^n, {n, 0, nn}], {x, 0, nn}], x] (* Michael De Vlieger, Sep 04 2016 *) PROG (Python) import math def binomial(n, m): ...a=1 ...for k in range(n-m+1, n+1): ......a *= k ...return a//math.factorial(m) def A127548(n): ...if n == 0: ......return 1 ...a=0 ...for s in range(1, n+1): ......a += (-1)**(n-s)*binomial(s+n-1, 2*s-1)*math.factorial(s) ...return a for n in range(0, 30): ...print(A127548(n)) # R. J. Mathar, Oct 20 2009 CROSSREFS Cf. A000179, A078480, A013999, A000271, A000904, A078509. Sequence in context: A060905 A304473 A174123 * A331326 A122835 A013185 Adjacent sequences:  A127545 A127546 A127547 * A127549 A127550 A127551 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jun 27 2007 EXTENSIONS More terms from R. J. Mathar, Jul 13 2007 More terms from R. J. Mathar, Oct 20 2009 STATUS approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)