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URL: https://oeis.org/A107883

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A107883
Column 3 of triangle A107880.
4
1, 2, 9, 61, 550, 6195, 83837, 1326923, 24078588, 493309850, 11271757335, 284379843234, 7856320956198, 235986714918110, 7660827258318780, 267365373971139600, 9985779421324740445, 397508459931685273305
OFFSET
0,2
FORMULA
G.f.: 1 = Sum_{k>=0} a(k)*x^k*(1-x)^((k+2)*(k+3)/2 - 1).
EXAMPLE
1 = 1*(1-x)^2 + 2*x*(1-x)^5 + 9*x^2*(1-x)^9 +
61*x^3*(1-x)^14 + 550*x^4*(1-x)^20 + 6195*x^5*(1-x)^27 +...
MATHEMATICA
a[ n_, k_: 0, j_: 2] := 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 *)
PROG
(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^((k+2)*(k+3)/2-1)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 04 2005
STATUS
approved