A324615 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n / A(x)^(n+1) * Product_{k=1..n} (1 + k*x).

1, 1, 1, 1, 1, 2, 3, 8, 17, 48, 128, 380, 1157, 3660, 12096, 40792, 143065, 511012, 1882800, 7070528, 27218600, 106809732, 427962654, 1746800424, 7262220721, 30724381288, 132185762998, 578077437072, 2567796553448, 11581814033420, 53009029679838, 246124348690992, 1158666578646045, 5528818866753080, 26729244857771670, 130885525083073344, 648916629598053632, 3256509647147411964, 16536590084997189054

Offset

0,6

Comments

a(n) is odd only when n is of the form 2^k or 3*2^k, or equal to 0 (conjecture).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 8*x^7 + 17*x^8 + 48*x^9 + 128*x^10 + 380*x^11 + 1157*x^12 + 3660*x^13 + 12096*x^14 + 40792*x^15 + ...
such that
1 = 1/A(x) + x*(1+x)/A(x)^2 + x^2*(1+x)*(1+2*x)/A(x)^3 + x^3*(1+x)*(1+2*x)*(1+3*x)/A(x)^4 + x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/A(x)^5 + x^5*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)/A(x)^6 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=0, #A, x^m*prod(k=1, m, 1 + k*x)/Ser(A)^(m+1)), #A-1); ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A029744.

Sequence in context: A148023 A148024 A148025 * A148026 A148027 A148028

Adjacent sequences: A324612 A324613 A324614 * A324616 A324617 A324618

Keyword

nonn

Author

Paul D. Hanna, Mar 19 2019

Status

approved