A107887 Column 2 of triangle A107884.

1, 3, 12, 67, 498, 4701, 54298, 745734, 11911221, 217418722, 4471886340, 102454974993, 2589782600870, 71643147090159, 2154145374733176, 69981625464827605, 2443741571641202568, 91309620200404008348

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)^(2+(k+1)*(k+2)/2).

Example

G.f. = 1 + 3*x + 12*x^2 + 67*x^3 + 498*x^4 + 4701*x^5 + 54298*x^6 + ...
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_: 2, 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 *)

Prog

(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(2+(k+1)*(k+2)/2)), n)}

Crossrefs

Cf. A107884, A107885, A107886, A107888.

Sequence in context: A337059 A294202 A107103 * A187118 A121812 A039750

Adjacent sequences: A107884 A107885 A107886 * A107888 A107889 A107890

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2005

Status

approved