A091725 -id:A091725 - cp's OEIS frontend

A093720 Decimal expansion of Sum_{n >= 2} zeta(n)/n!.

1, 0, 7, 8, 1, 8, 8, 7, 2, 9, 5, 7, 5, 8, 1, 8, 4, 8, 2, 7, 5, 8, 2, 6, 5, 4, 3, 6, 7, 6, 9, 8, 3, 2, 3, 8, 1, 7, 0, 7, 2, 1, 9, 6, 0, 9, 6, 7, 2, 3, 4, 7, 1, 6, 0, 0, 3, 7, 1, 7, 0, 2, 0, 7, 8, 0, 0, 7, 1, 5, 2, 3, 0, 0, 3, 2, 7, 8, 4, 3, 4, 8, 6, 5, 6, 7, 6, 7, 6, 8, 0, 8, 8, 5, 8, 2, 9, 0, 1

Offset: 1

Eric W. Weisstein, Apr 12 2004

			1.078188729575818482758265436769832381707219...

G. C. Greubel, Table of n, a(n) for n = 1..10000
J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

Cf. A076813, A093721, A269574, A269611, A269720, A269768.

evalf(Sum(exp(1/n)-1-1/n, n=1..infinity), 120); # Vaclav Kotesovec, Mar 04 2016

digits = 99; ClearAll[z, rd]; z[k_] := z[k] = z[k-1] + N[Sum[Zeta[n]/n!, {n, 2^(k-1) + 1, 2^k}], digits]; z[0] = 0; rd[k_] := rd[k] = RealDigits[z[k]][[1]]; rd[0]; rd[k = 1]; While[ rd[k] != rd[k-1], k++]; rd[k] (* Jean-François Alcover, Nov 09 2012 *)

suminf(n=2, zeta(n)/n!) \\ Michel Marcus, Mar 15 2017

Equals Sum_{k>=1} (exp(1/k) - 1 - 1/k). - Vaclav Kotesovec, Mar 04 2016

Equals Integral_{x=0..oo} exp(1/(x^2 + 1))*sin(x/(x^2 + 1))*(coth(Pi*x) - 1) dx + A091725 - 2*A001620 - exp(1)/2 + 3/2. - Velin Yanev, Nov 14 2024

Corrected by Fredrik Johansson, Mar 19 2006

A130744 a(n) = n(n+2)n!.

Original entry on oeis.org

0, 3, 16, 90, 576, 4200, 34560, 317520, 3225600, 35925120, 435456000, 5708102400, 80472268800, 1214269056000, 19527937228800, 333456963840000, 6025763487744000, 114887039275008000, 2304854534062080000

Offset: 0

Paul Curtz, Jul 12 2007

For n >= 1, a(n) = number whose factorial base representation (A007623) begins with a double digit {n}{n}, which is followed by n-1 zeros. Viewed in that base, this sequence looks like this: 0, 11, 220, 3300, 44000, 550000, 6600000, 77000000, 880000000, 9900000000, AA000000000, BB0000000000, ... (where "digits" A and B stand for placeholder values 10 and 11 respectively). - Antti Karttunen, May 07 2015

			G.f. = 3*x + 16*x^2 + 90*x^3 + 576*x^4 + 4200*x^5 + 34560*x^6 + ...

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for sequences related to factorial base representation.

Cf. A000142, A001048, A005563, A007623.
Column 3 of A257503 (apart from initial zero. Equally, row 3 of A257505).
Subsequence of both A227130 and A227148.
Cf. A001113, A001620, A091725, A099285.

[n*(n+2)*Factorial(n): n in [0..25]]; // Vincenzo Librandi, Aug 11 2011

a[n_]:=(n+2)!-(n+1)!-n!; (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)

a(n)=n!*(n*(n+2)) \\ Charles R Greathouse IV, Aug 11 2011

(define (A130744 n) (* n (+ 2 n) (A000142 n))) ;; Antti Karttunen, May 07 2015

0 = +a(n) * (+a(n+1) + 2*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+1) * (+5*a(n+2) - 6*a(n+3) + a(n+4)) + a(n+2) * (+3*a(n+2) - a(n+4)) + a(n+3) * (+a(n+3)) if n>=0. - Michael Somos, Mar 26 2014
From Antti Karttunen, May 07 2015: (Start)
a(n) = n * (n! + (n+1)!) = n * A001048(n+1).
a(n) = A005563(n) * A000142(n).
a(n) = (n+2)! - (n+1)! - n! [from Orlovsky's Mathematica-code].
(End)
From Amiram Eldar, May 17 2022: (Start)
Sum_{n>=1} 1/a(n) = (Ei(1) - gamma)/2 - 1/4, where Ei(1) = A091725 and gamma = A001620.
Sum_{n>=1} (-1)^(n+1)/a(n) = (gamma - Ei(-1))/2 - 1/e + 1/4, where Ei(-1) = -A099285 and e = A001113. (End)

More terms from Vladimir Joseph Stephan Orlovsky, Dec 05 2008

A001778 Lah numbers: a(n) = n!*binomial(n-1,5)/6!.

Original entry on oeis.org

1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800, 87265469491200, 2157837063782400, 55024845126451200, 1447576694865100800, 39291367432052736000, 1100158288097476608000, 31767070568814637056000

Offset: 6

N. J. A. Sloane

Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 6..100

Column 6 of A008297.
Column m=6 of unsigned triangle A111596.
Cf. A001113, A001620, A091725, A099285.

[Factorial(n-6)*Binomial(n,6)*Binomial(n-1,5): n in [6..30]]; // G. C. Greubel, May 10 2021

A001778 := proc(n)
    n!*binomial(n-1,5)/6! ;
end proc:
seq(A001778(n),n=6..30) ; # R. J. Mathar, Jan 06 2021

With[{c=6!},Table[n!Binomial[n-1,5]/c,{n,6,24}]] (* Harvey P. Dale, May 25 2011 *)

[binomial(n,6)*factorial(n-1)/factorial(5) for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009

E.g.f.: ((x/(1-x))^6)/6!.
If we define f(n,i,x) = Sum_{k=i..n} (Sum_{j=i..k} (binomial(k,j)*Stirling1(n,k) *Stirling2(j,i)*x^(k-j) ) ) then a(n) = (-1)^n*f(n,6,-6), (n>=6). - Milan Janjic, Mar 01 2009
D-finite with recurrence (-n+6)*a(n) +n*(n-1)*a(n-1)=0. - R. J. Mathar, Jan 06 2021
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=6} 1/a(n) = 570*(gamma - Ei(1)) + 1380*e - 2999, where gamma = A001620, Ei(1) = A091725 and e = A001113.
Sum_{n>=6} (-1)^n/a(n) = 15030*(gamma - Ei(-1)) - 9000/e - 8661, where Ei(-1) = -A099285. (End)

More terms from Christian G. Bower, Dec 18 2001

A001811 Coefficients of Laguerre polynomials.

Original entry on oeis.org

1, 25, 450, 7350, 117600, 1905120, 31752000, 548856000, 9879408000, 185513328000, 3636061228800, 74373979680000, 1586644899840000, 35272336619520000, 816302647480320000, 19645683716026368000, 491142092900659200000, 12740803704070041600000

Offset: 4

N. J. A. Sloane

			G.f. = x^4 + 25*x^5 + 450*x^6 + 7350*x^7 + 117600*x^8 + 1905120*x^9 + ...

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.
Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 4..100
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].
Cornelius Lanczos, Applied Analysis. (Annotated scans of selected pages)
Index entries for sequences related to Laguerre polynomials.

Cf. A053495.

Cf. A001113, A001620, A091725, A099285.

with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), right=Set(U, card=1)}, labeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=4..19) ; # Zerinvary Lajos, Feb 07 2008

Table[n! n (n - 1) (n - 2) (n - 3)/(4!)^2, {n, 4, 20}] (* T. D. Noe, Aug 10 2012 *)

[factorial(m) * binomial(m, 4) / 24 for m in range(4,19)] # Zerinvary Lajos, Jul 05 2008

a(n) = n!*n*(n-1)(n-2)(n-3)/(4!)^2. a(4)=1, a(n+1) = a(n) * (n+1)^2 / (n-3).
a(n) = A021009(n, 4), n >= 4.
E.g.f.: x^4/(4!*(1-x)^5).
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j) then a(n) = (-1)^n*f(n,4,-5), (n >= 4). - Milan Janjic, Mar 01 2009
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=4} 1/a(n) = 64*(Ei(1) - gamma - e) + 272/3, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=4} (-1)^n/a(n) = 544*(gamma - Ei(-1)) - 320/e - 944/3, where Ei(-1) = -A099285. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001

Corrected by T. D. Noe, Aug 10 2012

A052520 Number of pairs of sequences of cardinality at least 2.

Original entry on oeis.org

0, 0, 0, 0, 24, 240, 2160, 20160, 201600, 2177280, 25401600, 319334400, 4311014400, 62270208000, 958961203200, 15692092416000, 271996268544000, 4979623993344000, 96035605585920000, 1946321606541312000, 41359334139002880000, 919636959090769920000, 21356013827774545920000

Offset: 0

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 87.

Cf. sequences with formula (n + k)*n! listed in A282466.

Cf. A001113, A001620, A068985, A091725, A099285.

Concatenation([0,0,0,0], List([4..20], n-> (n-3)*Factorial(n))); # G. C. Greubel, May 13 2019

[n le 3 select 0 else (n-3)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 13 2019

spec := [S,{B=Sequence(Z,2 <= card),S=Prod(B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Table[Sum[n!, {i,4,n}], {n, 0, 19}] (* Zerinvary Lajos, Jul 12 2009 *)
With[{nn=20},CoefficientList[Series[x^4/(x-1)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 03 2016 *)

{a(n) = if(n<4, 0, (n-3)*n!)}; \\ G. C. Greubel, May 13 2019

[0,0,0,0]+[(n-3)*factorial(n) for n in (4..20)] # G. C. Greubel, May 13 2019

E.g.f.: x^4/(1-x)^2.
(n-3)*a(n+1) + (2+n-n^2)*a(n) = 0, with a(0) = a(1) = a(2) = a(3) = 0, a(4) = 24.
a(n) = (n-3)*n!, n>2.
a(n) = (n+1)!*(n-3)/(n+1), n>2. - Gary Detlefs, Oct 02 2011
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=4} 1/a(n) = 59/36 - 2*e/3 - gamma/6 + Ei(1)/6 = 59/36 - (2/3)*A001113 - (1/6)*A001620 + A091725/2.
Sum_{n>=4} (-1)^n/a(n) = 1/36 - 1/(3*e) + gamma/6 - Ei(-1)/6 = 1/36 - (1/3)*A068985 + (1/6)*A001620 + (1/6)*A099285. (End)

A062193 Fourth (unsigned) column sequence of triangle A062139 (generalized a=2 Laguerre).

Original entry on oeis.org

1, 24, 420, 6720, 105840, 1693440, 27941760, 479001600, 8562153600, 159826867200, 3116623910400, 63465795993600, 1348648164864000, 29877743960064000, 689322235650048000, 16543733655601152000, 412559358036553728000, 10678006913887272960000, 286526518855975157760000

Offset: 0

Wolfdieter Lang, Jun 19 2001

Harry J. Smith, Table of n, a(n) for n = 0..100
Index entries for sequences related to Laguerre polynomials.

Cf. A001710, A005990, A005461, A062139.

Cf. A001113, A001620, A091725, A099285.

[Factorial(n+3)*binomial(n+5, 5)/Factorial(3): n in [0..30]]; // G. C. Greubel, May 11 2018

With[{nn=20},CoefficientList[Series[(1+15*x+30*x^2+10*x^3)/(1-x)^9, {x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 02 2018 *)

{ f=2; for (n=0, 100, f*=n + 3; write("b062193.txt", n, " ", f*binomial(n + 5, 5)/6) ) } \\ Harry J. Smith, Aug 02 2009

my(x='x+O('x^30)); Vec(serlaplace((1+15*x+30*x^2+10*x^3)/(1-x)^9)) \\ G. C. Greubel, May 11 2018

[binomial(n,5)*factorial (n-2)/6 for n in range(5, 21)] # Zerinvary Lajos, Jul 07 2009

E.g.f.: (1+15*x+30*x^2+10*x^3)/(1-x)^9.
a(n) = A062139(n+3, 3).
a(n) = (n+3)!*binomial(n+5, 5)/3!.
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i)*x^(k-j) then a(n-3) = (-1)^(n-1)*f(n,3,-6), (n>=3). - Milan Janjic, Mar 01 2009
From Amiram Eldar, May 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 75*(Ei(1) - gamma) - 30*e - 65/4, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=0} (-1)^n/a(n) = 315*(gamma - Ei(-1)) - 180/e - 735/4, where Ei(-1) = -A099285. (End)

A111597 Lah numbers: a(n) = n!*binomial(n-1,6)/7!.

Original entry on oeis.org

1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 779155977600, 20777492736000, 565147802419200, 15721384321843200, 448059453172531200, 13097122477350912000, 392913674320527360000, 12101741169072242688000

Offset: 7

Wolfdieter Lang, Aug 23 2005

Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.

G. C. Greubel, Table of n, a(n) for n = 7..440

Column 7 of A008297 and unsigned A111596.
Column 6 of A001778.
Cf. A001113, A001620, A091725, A099285.

[Factorial(n-7)*Binomial(n, 7)*Binomial(n-1, 6): n in [7..30]]; // G. C. Greubel, May 10 2021

k = 7; a[n_] := n!*Binomial[n-1, k-1]/k!; Table[a[n], {n, k, 22}]  (* Jean-François Alcover, Jul 09 2013 *)

[factorial(n-7)*binomial(n, 7)*binomial(n-1, 6) for n in (7..30)] # G. C. Greubel, May 10 2021

E.g.f.: ((x/(1-x))^7)/7!.
a(n) = (n!/7!)*binomial(n-1, 7-1).
If we define f(n,i,x) = Sum_{k=i..n} (Sum_{j=i..k} (binomial(k,j)*Stirling1(n,k)* Stirling2(j,i)*x^(k-j) ) ) then a(n+1) = (-1)^n*f(n,6,-8), (n>=6). - Milan Janjic, Mar 01 2009
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=7} 1/a(n) = 6342*(Ei(1) - gamma) - 8988*e + 80374/5, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=7} (-1)^(n+1)/a(n) = 170142*(gamma - Ei(-1)) - 101640/e - 490714/5, where Ei(-1) = -A099285. (End)

A208528 Number of permutations of n>1 having exactly 3 points P on the boundary of their bounding square.

Original entry on oeis.org

0, 4, 16, 72, 384, 2400, 17280, 141120, 1290240, 13063680, 145152000, 1756339200, 22992076800, 323805081600, 4881984307200, 78460462080000, 1339058552832000, 24186745110528000, 460970906812416000, 9245027631071232000, 194632160654131200000

Offset: 2

David Nacin, Feb 27 2012

nonn

A bounding square for a permutation of n is the square with sides parallel to the coordinate axis containing (1,1) and (n,n), and the set of points P of a permutation p is the set {(k,p(k)) for 0

a(n) is the number of permutations of n symbols that 3-commute with a transposition (see A233440 for definition): a permutation p of {1,...,n} has exactly three points on the boundary of their bounding square if and only if p 3-commutes with transposition (1, n). - Luis Manuel Rivera Martínez, Feb 27 2014

			a(3) = 4 because {(1,1),(2,3),(3,2)}, {(1,3),(2,1),(3,2)}, {(1,2),(2,3),(3,1)} and {(1,2),(2,1),(3,3)} each have three points on the bounding square.

Vincenzo Librandi, Table of n, a(n) for n = 2..200
Emeric Deutsch, Permutations and their bounding squares, Math Magazine, 85(1) (2012), p. 63.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

Cf. A098916, A208529.

Cf. A001620, A091725, A099285.

Mathematica
```
Table[(4n-8)(n-2)!, {n, 2, 10}]
```

import math
def a(n):
    return (4*n-8)*math.factorial(n-2)

a(n) = (4*n-8) * (n-2)!
From Amiram Eldar, May 17 2022: (Start)
Sum_{n>=3} 1/a(n) = (Ei(1) - gamma)/4, where Ei(1) = A091725 and gamma = A001620.
Sum_{n>=3} (-1)^(n+1)/a(n) = (gamma - Ei(-1))/4, where Ei(-1) = -A099285. (End)

A001812 Coefficients of Laguerre polynomials.

Original entry on oeis.org

1, 36, 882, 18816, 381024, 7620480, 153679680, 3161410560, 66784798080, 1454424491520, 32724551059200, 761589551923200, 18341615042150400, 457129482588979200, 11787410229615820800, 314330939456421888000, 8663746518767628288000, 246661959710796005376000

Offset: 5

N. J. A. Sloane

nonn

			G.f. = x^5 + 36*x^6 + 882*x^7 + 18816*x^8 + 381024*x^9 + 7620480*x^10 + ...

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.
Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 5..100
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].
Cornelius Lanczos, Applied Analysis (Annotated scans of selected pages)
Index entries for sequences related to Laguerre polynomials.

Cf. A001113, A001620, A021009, A091725, A099285.

[((Factorial(n)/Factorial(5))^2)/Factorial(n-5): n in [5..20]]; // G. C. Greubel, May 11 2018

Table[((n!/5!)^2)/(n-5)!, {n, 5, 20}] (* T. D. Noe, Aug 10 2012 *)

for(n=5,20, print1(((n!/5!)^2)/(n-5)!, ", ")) \\ G. C. Greubel, May 11 2018

[factorial(m) * binomial(m, 5) / 120 for m in range(5,23)] # Zerinvary Lajos, Jul 05 2008

a(n) = (-1)*A021009(n, 5), n >= 5.
a(n) = ((n!/5!)^2)/(n-5)!, n >= 5.
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i)*x^(k-j) then a(n) = (-1)^(n-1)*f(n,5,-6), (n>=5). - Milan Janjic, Mar 01 2009
From Amiram Eldar, May 02 2022: (Start)
Sum_{n>=5} 1/a(n) = 375*(gamma - Ei(1)) + 150*e + 175/2, where e = A001113, gamma = A001620, and Ei(1) = A091725.
Sum_{n>=5} (-1)^(n+1)/a(n) = 5225*(gamma - Ei(-1)) - 3100/e - 18125/6, where Ei(-1) = -A099285. (End)

A052521 Number of pairs of sequences of cardinality at least 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 720, 10080, 120960, 1451520, 18144000, 239500800, 3353011200, 49816166400, 784604620800, 13076743680000, 230150688768000, 4268249137152000, 83230858174464000, 1703031405723648000

Offset: 0

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

G. C. Greubel, Table of n, a(n) for n = 0..445
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 88.

Cf. sequences with formula (n + k)*n! listed in A282466.

Cf. A001113, A001620, A068985, A091725, A099285.

Concatenation([0,0,0,0,0,0], List([6..20], n-> (n-5)*Factorial(n))); # G. C. Greubel, May 13 2019

[n le 5 select 0 else (n-5)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 13 2019

spec := [S,{B=Sequence(Z,3 <= card), S=Prod(B,B)},labeled]: # Pairs spec
seq(combstruct[count](spec, size=n), n=0..20);

Table[If[n<6, 0, (n-5)*n!], {n,0,20}] (* G. C. Greubel, May 13 2019 *)

{a(n) = if(n<6, 0, (n-5)*n!)}; \\ G. C. Greubel, May 13 2019

[0,0,0,0,0,0]+[(n-5)*factorial(n) for n in (6..20)] # G. C. Greubel, May 13 2019

E.g.f.: x^6/(1-x)^2.
(n-5)*a(n+1) + (4 + 3*n - n^2)*a(n) = 0, with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = 0, a(6) = 720.
a(n) = (n-5)*n!.
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=6} 1/a(n) = 5477/7200 - 17*e/60 - gamma/120 + Ei(1)/120 = 5477/7200 - (17/60)*A001113 - (1/120)*A001620 + A091725/120.
Sum_{n>=6} (-1)^n/a(n) = 403/7200 - 1/(6*e) + gamma/120 - Ei(-1)/120 = 403/7200 - (1/6)*A068985 + (1/120)*A001620 + (1/120)*A099285. (End)

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cp's OEIS Frontend

A093720 Decimal expansion of Sum_{n >= 2} zeta(n)/n!.

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A130744 a(n) = n*(n+2)*n!.

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Magma

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A001778 Lah numbers: a(n) = n!*binomial(n-1,5)/6!.

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Sage

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A001811 Coefficients of Laguerre polynomials.

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A052520 Number of pairs of sequences of cardinality at least 2.

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A062193 Fourth (unsigned) column sequence of triangle A062139 (generalized a=2 Laguerre).

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A130744 a(n) = n(n+2)n!.