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A154286 a(n) = E(k)C(n+k,k) = Euler(k)*Pascal(n+k,k) for k=4. 14
5, 25, 75, 175, 350, 630, 1050, 1650, 2475, 3575, 5005, 6825, 9100, 11900, 15300, 19380, 24225, 29925, 36575, 44275, 53130, 63250, 74750, 87750, 102375, 118755, 137025, 157325, 179800, 204600, 231880, 261800, 294525, 330225, 369075, 411255 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

+ a(n) = E(4)binom{n+4}{4} where E(n) are the Euler number in the enumeration A122045.

+ a(n) is the special case k=4 in the sequence of diagonals in the triangle A153641.

+ a(n) is the 5th row in A093375.

+ a(n) is the 5th column in A103406.

+ a(n) is the 5th antidiagonal in A103283.

+ (a(n+1)-a(n))/5 are the pyramidal numbers A000292 (n>1).

+ (a(n+2)-2a(n+1)+a(n))/5 are the triangular numbers A000217 (n>2).

+ (a(n+3)-3a(n+2)+3a(n+1)-a(n))/5 are the natural numbers A000027 (n>3).

Number of orbits of Aut(Z^7) as function of the infinity norm (n+4) of the representative integer lattice point of the orbit, when the cardinality of the orbit is equal to 107520. - Philippe A.J.G. Chevalier, Dec 28 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (n+1)*(n+2)*(n+3)*(n+4)*5/24.

a(n) = a(n-1)*(n+4)/n (n>0), a(0)=5.

O.g.f.: 5/(1-x)^5.

E.g.f.: (5/24)*x*(24 + 36*x + 12*x^2 + x^3)*exp(x). - G. C. Greubel, Sep 09 2016

a(n) = 5*A000332(n+4). - Michel Marcus, Sep 10 2016

MAPLE

seq(euler(4)*binomial(n+4, 4), n=0..32);

MATHEMATICA

CoefficientList[Series[-5/(x - 1)^5, {x, 0, 35}], x] (* Robert G. Wilson v, Jan 29 2015 *)

Table[(n + 1)*(n + 2)*(n + 3)*(n + 4)*5/24, {n, 0, 25}] (* G. C. Greubel, Sep 09 2016 *)

PROG

(MAGMA) [(n+1)*(n+2)*(n+3)*(n+4)*5 div 24: n in [0..40]]; // Vincenzo Librandi, Sep 10 2016

(PARI) x='x+O('x^99); Vec(5/(1-x)^5) \\ Altug Alkan, Sep 10 2016

CROSSREFS

Cf. A000217, A153641, A000579.

Sequence in context: A146665 A059302 A147130 * A078234 A056374 A171272

Adjacent sequences:  A154283 A154284 A154285 * A154287 A154288 A154289

KEYWORD

easy,nonn

AUTHOR

Peter Luschny, Jan 06 2009

STATUS

approved

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Last modified February 25 04:05 EST 2018. Contains 299630 sequences. (Running on oeis4.)