A305600 G.f. A(x) satisfies: [x^k] (1+x)^(n^2) * A(x) = 0 for k = (n-1)^2 + 1 through k = n^2 for n >= 1.

1, -1, -2, 10, -25, 33, 57, -561, 2310, -7150, 18448, -39168, 55114, 41990, -726750, 3657006, -13846041, 44907185, -130605450, 347227650, -845335695, 1842623895, -3311675445, 3271798125, 9143639100, -77910795756, 356581496251, -1331363100907, 4430526577054, -13595755404934, 39119816049161, -106498829726801, 275433122695473, -676162020887697, 1563087628000497, -3329539580829865, 6175049600047825

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..2500

Prog

(PARI) /* Informal code to generate terms */
{A=[1, -1]; for(i=1, 400, A=concat(A, 0); m=sqrtint(#A-2)+1; A[#A] = -polcoeff( (1+x +x*O(x^#A))^(m^2)*Ser(A), #A-1) ; print1(#A, ", ")); A}
/* Show that the definition is satisfied: */
for(n=1, sqrtint(#A), print1(n": "); for(k=(n-1)^2+1, n^2, print1(polcoeff( (1+x+x*O(x^#A))^(n^2)*Ser(A) , k), ", ")); print(""))

Crossrefs

Sequence in context: A248117 A345695 A336958 * A058373 A167386 A027719

Adjacent sequences: A305597 A305598 A305599 * A305601 A305602 A305603

Keyword

sign

Author

Paul D. Hanna, Jun 13 2018

Status

approved