A350524 G.f. A(x) satisfies: [x^(2*n-2)] A(x)^(n^2) = 0 and [x^(2*n-1)] A(x)^(n^2) = 0 for n > 1, with a(0) = 1, a(2) = 2.

1, 2, -6, 28, -144, 736, -3512, 14896, -61600, 509632, -12903296, 422568704, -17796848640, 824388274176, -43343785743488, 2375499099860224, -140774447935008256, 8727751762659943424, -578377033389467758592, 40230774454685666598912, -2967831511563656631672832, 229648123356288830870929408

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Example

G.f.: A(x) = 1 + 2*x - 6*x^2 + 28*x^3 - 144*x^4 + 736*x^5 - 3512*x^6 + 14896*x^7 - 61600*x^8 + 509632*x^9 - 12903296*x^10 + ...
The table of coefficients of x^k in A(x)^(n^2), for k>=0, begins:
n=1: [1, 2, -6, 28, -144, 736, -3512, 14896, -61600, 509632, ...];
n=2: [1, 8, 0, 0, 40, -512, 4608, -32768, 152272, 456064, ...];
n=3: [1, 18, 90, 60, 0, 0, -1176, 20592, -278208, 3442304, ...];
n=4: [1, 32, 384, 2048, 4256, 1792, 0, 0, -36672, 621568, ...];
n=5: [1, 50, 1050, 11900, 77600, 285760, 537000, 399600, 0, 0, ...];
n=6: [1, 72, 2304, 43008, 516456, 4147200, 22411776, 79921152, 178965072, 227782016, 0, 0, ...]; ...
in which both coefficients of x^(2*n-2) and x^(2*n-1) in A(x)^(n^2) equal zero for n > 1.

Prog

(PARI) {a(n) = my(A=[1, 2], P); for(i=1, n, A=concat(A, 0); P = (#A+1)\2;
A[#A] = -polcoeff( Ser(A)^(P^2)/(P^2), #A-1) ); H=A; A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A171791, A350525.

Sequence in context: A227294 A302336 A225877 * A228842 A218941 A303829

Adjacent sequences: A350521 A350522 A350523 * A350525 A350526 A350527

Keyword

sign

Author

Paul D. Hanna, Jan 03 2022

Status

approved