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A113135 a(0) = a(1) = 1, a(2) = x, a(3) = 2x^2, a(n) = x*(n-1)*a(n-1) + Sum_{j=2..n-2} (j-1)*a(j)*a(n-j), n>=4 and for x = 8. 7
1, 1, 8, 128, 3136, 103424, 4270080, 211107840, 12135936000, 794618298368, 58355305676800, 4749550536359936, 424336070117163008, 41287521140173963264, 4346005245162898325504, 492102089936714946576384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n+1) = Sum{k, 0<=k<=n} 8^k*A113129(n, k).

G.f.: A(x) = x/series_reversion(x*G(x)) where G(x) = g.f. of 8-fold factorials.

G.f. satisfies: A(x*G(x)) = G(x) = g.f. of 8-fold factorials.

EXAMPLE

a(2) = 8.

a(3) = 2*8^2 = 128.

a(4) = 8*3*128 + 1*8*8 = 3136.

a(5) = 8*4*3136 + 1*8*128 + 2*128*8 = 103424.

a(6) = 8*5*103424 + 1*8*3136 + 2*128*128 + 3*3136*8 = 4270080

G.f.: A(x) = 1 + x + 8*x^2 + 128*x^3 + 3136*x^4 + 103424*x^5 +...

= x/series_reversion(x + x^2 + 9*x^3 + 153*x^4 + 3825*x^5 +...).

MATHEMATICA

x=8; a[0]=a[1]=1; a[2]=x; a[3]=2x^2; a[n_]:=a[n]=x*(n-1)*a[n-1]+Sum[(j-1)*a[j ]*a[n-j], {j, 2, n-2}]; Table[a[n], {n, 0, 16}](Robert G. Wilson v)

PROG

(PARI) a(n)=Vec(x/serreverse(x*Ser(vector(n+1, k, if(k==1, 1, prod(j=0, k-2, 8*j+1))))))[n+1]

(PARI) a(n, x=8)=if(n<0, 0, if(n==0 || n==1, 1, if(n==2, x, if(n==3, 2*x^2,

x*(n-1)*a(n-1)+sum(j=2, n-2, (j-1)*a(j)*a(n-j))))))

CROSSREFS

Cf. A045755, A075834(x=1), A111088(x=2), A113130(x=3), A113131(x=4), A113132(x=5), A113133(x=6), A113134(x=7).

Sequence in context: A237023 A156270 A051189 * A219264 A188060 A104997

Adjacent sequences:  A113132 A113133 A113134 * A113136 A113137 A113138

KEYWORD

nonn

AUTHOR

Philippe Deléham and Paul D. Hanna, Oct 28 2005

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)