A363543 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3^k + A(x^k)) * x^k/k ).

1, 4, 7, 23, 69, 234, 826, 3000, 11168, 42313, 162829, 634052, 2495051, 9903761, 39612048, 159481988, 645833656, 2628829700, 10749777653, 44139474552, 181916530895, 752288709592, 3120574260606, 12981015704961, 54138655342763, 226330448292140

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

A(x) = Sum_{k>=0} a(k) * x^k = (1+3*x) * Product_{k>=0} (1+x^(k+1))^a(k).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( (-3)^k + Sum_{d|k} (-1)^(k/d) * d * a(d-1) ) * a(n-k).

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(3^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A038075, A363542.

Cf. A363509, A363541.

Sequence in context: A270238 A027946 A348478 * A242315 A275313 A288299

Adjacent sequences: A363540 A363541 A363542 * A363544 A363545 A363546

Keyword

nonn

Author

Seiichi Manyama, Jun 09 2023

Status

approved