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A107878
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Column 2 of triangle A107876.
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6
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1, 1, 3, 15, 106, 975, 11100, 151148, 2401365, 43681578, 896371205, 20504034645, 517705752096, 14310162565395, 430020328711305, 13963933247986995, 487456219774434795, 18209055555140970945, 724952705958984299025
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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G.f.: 1 = Sum_{k>=0} a(k)*x^k*(1-x)^((k+1)*(k+2)/2).
From Benedict W. J. Irwin, Nov 29 2016: (Start)
Conjecture: a(n) is given by a series of nested sums,
a(1) = Sum_{i=1..1} 1,
a(2) = Sum_{i=1..1}Sum_{j=1..i+2} 1,
a(3) = Sum_{i=1..1}Sum_{j=1..i+2}Sum_{k=1..j+3} 1,
a(4) = Sum_{i=1..1}Sum_{j=1..i+2}Sum_{k=1..j+3}Sum_{l=1..k+4} 1. (End)
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EXAMPLE
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G.f. = 1 + x + 3*x^2 + 15*x^3 + 106*x^4 + 975*x^5 + 11100*x^6 + 151148*x^7 + ...
1 = 1*(1-x)^1 + 1*x*(1-x)^3 + 3*x^2*(1-x)^6 + 15*x^3*(1-x)^10 + 106*x^4*(1-x)^15 + 975*x^5*(1-x)^21 + 11100*x^6*(1-x)^21 +...
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MATHEMATICA
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a[ n_, k_: 0, j_: 1] := If[ n < 1, Boole[n >= 0], a[ n, k, j] = Sum[ a[ n - 1, i, j + 1], {i, k + j}]]; (* Michael Somos, Nov 26 2016 *)
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PROG
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(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^((k+1)*(k+2)/2)), n)}
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CROSSREFS
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Cf. A107876, A107877, A107879, A209440 (variant).
Sequence in context: A353587 A128276 A295124 * A218688 A120016 A349874
Adjacent sequences: A107875 A107876 A107877 * A107879 A107880 A107881
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jun 04 2005
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STATUS
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approved
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