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Search: id:A113134
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| A113134 |
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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 = 7. |
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8
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| 1, 1, 7, 98, 2107, 61054, 2215094, 96203268, 4856212179, 279081882086, 17981777803682, 1283631249683804, 100557420457355358, 8577121056958121836, 791318123914138366924, 78521346319092948749576
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n+1) = Sum{k, 0<=k<=n} 7^k*A113129(n, k).
G.f.: A(x) = x/series_reversion(x*G(x)) where G(x) = g.f. of 7-fold factorials.
G.f. satisfies: A(x*G(x)) = G(x) = g.f. of 7-fold factorials.
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EXAMPLE
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a(2) = 7.
a(3) = 2*7^2 = 98.
a(4) = 7*3*98 + 1*7*7 = 2107.
a(5) = 7*4*2107 + 1*7*98 + 2*98*7 = 61054.
a(6) = 7*5*61054 + 1*7*2107 + 2*98*98 + 3*2107*7 = 2215094.
G.f.: A(x) = 1 + x + 7*x^2 + 98*x^3 + 2107*x^4 + 61054*x^5
+...
= x/series_reversion(x + x^2 + 8*x^3 + 120*x^4 + 2640*x^5
+...).
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MATHEMATICA
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x=7; 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 (rgwv(AT)rgwv.com))
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PROGRAM
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(PARI) {a(n)=Vec(x/serreverse(x*Ser(vector(n+1, k, if(k==1, 1, prod(j=0, k-2, 7*j+1))))))[n+1]}
(PARI) {a(n, x=7)=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))))))}
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CROSSREFS
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Cf. A045754, A075834(x=1), A111088(x=2), A113130(x=3), A113131(x=4), A113132(x=5), A113133(x=6), A113135(x=8).
Sequence in context: A133679 A156266 A051188 this_sequence A092818 A041087 A041084
Adjacent sequences: A113131 A113132 A113133 this_sequence A113135 A113136 A113137
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2005
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