A360896 -id:A360896 - cp's OEIS frontend

A360885 G.f. satisfies A(x) = 1 + x * A(x * (1 + x^2)).

1, 1, 1, 1, 2, 4, 7, 16, 39, 93, 246, 671, 1884, 5578, 16887, 52854, 170649, 563703, 1914366, 6649798, 23610987, 85689987, 317054427, 1196183592, 4595744763, 17965311672, 71426213637, 288535755417, 1183807706841, 4929801601890, 20825803784129, 89210585925338

Offset: 0

Seiichi Manyama, Feb 25 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..934

Cf. A127782, A360886.

Cf. A360896.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-1-2*j, j)*v[i-2*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1-2*k,k) * a(n-1-2*k).

A360894 G.f. satisfies A(x) = 1 + x * A(x * (1 - x)).

Original entry on oeis.org

1, 1, 1, 0, -2, -1, 7, 0, -44, 69, 276, -1471, 675, 20407, -90560, -20552, 2141700, -10558223, -675239, 329376824, -2106253225, 2364924062, 67114942438, -621638176430, 1926931098484, 14768396756732, -236623058229675, 1371752460097440, 1098671590491324

Offset: 0

Seiichi Manyama, Feb 25 2023

sign

Cf. A360896, A360897.

Cf. A127782.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (-1)^j*binomial(i-1-j, j)*v[i-j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1-k,k) * a(n-1-k).

A360897 G.f. satisfies A(x) = 1 + x * A(x * (1 - x^3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 0, -2, -5, -9, -8, 7, 48, 120, 161, -18, -798, -2486, -4088, -692, 19840, 71159, 130467, 31737, -688014, -2644266, -5066453, -866551, 31217375, 121457519, 231494879, -10834753, -1756652362, -6638239650, -12044755426, 5372265122, 117373545212

Offset: 0

Seiichi Manyama, Feb 25 2023

sign

Cf. A360894, A360896.

Cf. A360886.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, (-1)^j*binomial(i-1-3*j, j)*v[i-3*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} (-1)^k * binomial(n-1-3*k,k) * a(n-1-3*k).

cp's OEIS Frontend

A360885 G.f. satisfies A(x) = 1 + x * A(x * (1 + x^2)).

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A360894 G.f. satisfies A(x) = 1 + x * A(x * (1 - x)).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A360897 G.f. satisfies A(x) = 1 + x * A(x * (1 - x^3)).

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Author

Keywords

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Programs

PARI

Formula