A377964
Expansion of e.g.f. (1+x) * exp(x*(1+x)^3).
Original entry on oeis.org
1, 2, 9, 58, 389, 3186, 29437, 294554, 3233673, 38350594, 484794641, 6522118362, 92857444429, 1390937221298, 21858658599429, 359271578140666, 6156249977141777, 109722278546645634, 2029772196329985433, 38893956306343711994, 770622936760496106261, 15763542538016019828082
Offset: 0
-
a(n, s=1, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
A377965
Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^2).
Original entry on oeis.org
1, 3, 11, 55, 309, 1931, 13543, 101991, 828425, 7192819, 66002691, 639830423, 6510397501, 69266297595, 768989536799, 8876171274631, 106301772962193, 1318277355041891, 16892429768517115, 223330116792810999, 3041570471301007301, 42611228176879105003
Offset: 0
-
a(n, s=2, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
A378019
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x) ).
Original entry on oeis.org
1, 2, 9, 79, 957, 15441, 309943, 7468301, 210221385, 6774449185, 246049105131, 9947338595085, 443121311695021, 21568178966624993, 1138938283455953919, 64856665518838006861, 3961941908569940501649, 258453847468153873181889, 17932482767578645884498643
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)*exp(-lambertw(-x*(1+x)^2))))
-
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(2*k+1, n-k)/k!);
Showing 1-3 of 3 results.