A349036 -id:A349036 - cp's OEIS frontend

A349035 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-2*x)).

1, 1, 2, 1, 9, 6, 165, 97, 10970, 8617, 2838793, 1206206, 2912348749, 3338391105, 11938619074866, -3485058191151, 195607339607544393, 505337929567029942, 12820529140255160177781, -40595263531274884237983, 3360756421633193695872693450

Offset: 0

Ilya Gutkovskiy, Nov 06 2021

sign

Cf. A001006, A015097, A348878, A349036, A349037.

nmax = 20; A[] = 0; Do[A[x] = 1/(1 - x - x^2 A[-2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-2)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} (-2)^k * a(k) * a(n-k-2).

A349037 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-4*x)).

Original entry on oeis.org

1, 1, 2, -1, 29, 116, 7701, -103563, 31343898, 1759289595, 2057705197793, -457070362176172, 2156748187140412361, 1921405067209313680505, 36188075164863127910696914, -128870933294125665748520896793, 9713904752944734908048841134573557

Offset: 0

Ilya Gutkovskiy, Nov 06 2021

sign

Cf. A001006, A015099, A348880, A349035, A349036.

nmax = 16; A[] = 0; Do[A[x] = 1/(1 - x - x^2 A[-4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-4)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 16}]

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} (-4)^k * a(k) * a(n-k-2).

cp's OEIS Frontend

A349035 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-2*x)).

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