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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

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

Cf. A107880, A107881, A107882.

Sequence in context: A289713 A053983 A192939 * A088182 A006155 A121870

Adjacent sequences:  A107880 A107881 A107882 * A107884 A107885 A107886

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 04 2005

STATUS

approved

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Last modified February 19 14:22 EST 2018. Contains 299333 sequences. (Running on oeis4.)