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A274268 E.g.f. (1 + x)^4*log(1 + x). 4
1, 7, 26, 50, 24, -24, 48, -144, 576, -2880, 17280, -120960, 967680, -8709120, 87091200, -958003200, 11496038400, -149448499200, 2092278988800, -31384184832000, 502146957312000, -8536498274304000, 153656968937472000, -2919482409811968000, 58389648196239360000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First five terms [1, 7, 26, 50, 24] form row 4 of A105954 read as a triangular array.

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n) = (-1)^(n-1)*24*(n - 5)! for n >= 5.

E.g.f. A(x) = (1 + x)^4*log(1 + x) = x + 7*x^2/2 + 26*x^3/3! + 50*x^4/4! + 24*x^5/5! - 24*x^6/6! + ....

Series reversion(A(x)) = exp(-1/4*T(-4*x)) - 1 = x - 7*x^2/2! + 11^2*x^3/3! - 15^3*x^4/4! + 19^4*x^5/5! - ... is the e.g.f. for a signed version of A274267, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.

MATHEMATICA

CoefficientList[Series[(1+t)^4 * Log[1+t], {t, 1, 20}], t]*Range[1, 20]! (* G. C. Greubel, Jun 19 2016 *)

PROG

(MAGMA) [1, 7, 26, 50] cat [(-1)^(n-1)*24*Factorial(n-5): n in [5..25]]; // Vincenzo Librandi, Jun 20 2016

CROSSREFS

Cf. A000169, A105954, A274265, A274266, A274267, A274268, A274269, A274270.

Sequence in context: A063153 A063578 A063159 * A059376 A206481 A049453

Adjacent sequences:  A274265 A274266 A274267 * A274269 A274270 A274271

KEYWORD

sign,easy

AUTHOR

Peter Bala, Jun 19 2016

STATUS

approved

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Last modified September 23 15:54 EDT 2017. Contains 292361 sequences.