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A226738 Row 3 of array in A226513. 4
1, 4, 24, 184, 1704, 18424, 227304, 3147064, 48278184, 812387704, 14872295784, 294192418744, 6251984167464, 142032703137784, 3434617880825064, 88075274293319224, 2387099326339205544, 68177508876215724664, 2046501717592969431144, 64408432189100396344504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Connor Ahlbach, Jeremy Usatine and Nicholas Pippenger, Barred Preferential Arrangements, Electron. J. Combin., Volume 20, Issue 2 (2013), #P55.

FORMULA

E.g.f.: 1/(2 - exp(x))^4 (see the Ahlbach et al. paper, Theorem 4).

a(n) = sum( S2(n,i)*i!*binomial(3+i,i), i=0..n ), where S2 is the Stirling number of the second kind (see the Ahlbach et al. paper, Theorem 3). [Bruno Berselli, Jun 18 2013]

G.f.: 1/T(0), where T(k) = 1 - x*(k+4)/(1 - 2*x*(k+1)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 28 2013

MATHEMATICA

Range[0, 20]! CoefficientList[Series[(2 - Exp@x)^-4, {x, 0, 20}], x]

PROG

(MAGMA) m:=3; [&+[StirlingSecond(n, i)*Factorial(i)*Binomial(m+i, i): i in [0..n]]: n in [0..20]]; // Bruno Berselli, Jun 18 2013

CROSSREFS

Cf. rows 0, 1, 2, 4, 5 of A226513: A000670, A005649, A226515, A226739, A226740.

Sequence in context: A152403 A111556 A300736 * A271215 A135905 A239296

Adjacent sequences:  A226735 A226736 A226737 * A226739 A226740 A226741

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Jun 18 2013

STATUS

approved

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)