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A321850 E.g.f.: exp(x/(1-7*x)). 5
1, 1, 15, 337, 10081, 376461, 16849351, 878797165, 52324954977, 3501300491641, 260062721279551, 21228108532279881, 1888618754806601665, 181873163575529411077, 18846187172580219099831, 2090754000231731874682021, 247221828043044971020645441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For k = 2,3,4,... the difference a(n+k) - a(n) is divisible by k.

LINKS

Ludovic Schwob, Table of n, a(n) for n = 0..199

FORMULA

a(n) = Sum_{k=0..n} 7^(n-k)*(n!/k!)*binomial(n-1, k-1).

Recurrence: a(n) = (14*n-13)*a(n-1) - 49*(n-2)*(n-1)*a(n-2).

a(n) ~ n! * exp(2*sqrt(n/7) - 1/14) * 7^(n - 1/4) / (2 * sqrt(Pi) * n^(3/4)). - Vaclav Kotesovec, Nov 21 2018

MAPLE

seq(coeff(series(factorial(n)*exp(x/(1-7*x)), x, n+1), x, n), n = 0 .. 17); # Muniru A Asiru, Nov 24 2018

MATHEMATICA

a[n_] := Sum[7^(n - k)*n!/k!*Binomial[n - 1, k - 1], {k, 0, n}]; Array[a, 20, 0] (* or *) a[0] = a[1] = 1; a[n_] := a[n] = (14n - 13)*a[n - 1] - 49(n - 2)(n - 1)*a[n - 2]; Array[a, 20, 0] (* Amiram Eldar, Nov 19 2018 *)

PROG

(PARI) my(x='x + O('x^20)); Vec(serlaplace(exp(x/(1-7*x)))) \\ Michel Marcus, Nov 25 2018

(MAGMA) [1] cat [&+[7^(n-k)*Factorial(n)/Factorial(k)*Binomial(n-1, k-1):  k in [0..n]]: n in [1.. 18]]; // Vincenzo Librandi, Dec 08 2018

CROSSREFS

Cf. A000262, A025168, A321837, A321847, A321848, A321849.

Sequence in context: A114937 A289180 A157965 * A100875 A286391 A034975

Adjacent sequences:  A321847 A321848 A321849 * A321851 A321852 A321853

KEYWORD

nonn

AUTHOR

Ludovic Schwob, Nov 19 2018

STATUS

approved

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Last modified February 22 15:05 EST 2020. Contains 332137 sequences. (Running on oeis4.)