A356409
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^(1/(1-x)).
Original entry on oeis.org
1, 1, 5, 28, 203, 1756, 17802, 205010, 2644287, 37669096, 586855058, 9914829508, 180429770402, 3516313661706, 73029591042943, 1609531482261375, 37504691293842367, 920966310015565936, 23764054962685200642, 642681497080268685092, 18174504398294667649782
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k!)^(1/(1-x))))
-
a356407(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^d)));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356407(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356402
Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^(1/(1-x)).
Original entry on oeis.org
1, 1, 3, 16, 86, 626, 5267, 50793, 543279, 6544805, 86503762, 1242678141, 19259416827, 321457169151, 5736414618209, 108931865485750, 2191495621647324, 46604972526167314, 1043844453093239627, 24555321244430950299, 605239630722584461955, 15600222966916650541099
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^(1/(1-x))))
-
a356401(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!)));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356401(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356458
Expansion of e.g.f. ( Product_{k>0} B(x^k) )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.
Original entry on oeis.org
1, 1, 6, 38, 319, 3117, 36359, 476121, 7025708, 114118746, 2029450055, 39078892305, 810834093733, 17998186069489, 425672049713174, 10676653292086790, 283014906314277059, 7901659174554937925, 231719030698518379003, 7118469816302381503209
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k)-1))^(1/(1-x))))
-
a355886(n) = n!*sum(k=1, n, n\k/k!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a355886(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356461
Expansion of e.g.f. ( Product_{k>0} B(x^k)^k )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.
Original entry on oeis.org
1, 1, 8, 62, 631, 7417, 104489, 1648845, 29319588, 572982162, 12250559615, 283321630605, 7053444523393, 187711377451249, 5317981377046420, 159652557864884330, 5061465465801168419, 168886786171198864725, 5914650120884760212977, 216844308186908733542877
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k)-1)^k)^(1/(1-x))))
-
a356459(n) = n!*sum(k=1, n, sumdiv(k, d, d/(k/d)!));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356459(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356575
Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^x.
Original entry on oeis.org
1, 0, 2, 6, 24, 185, 990, 9877, 72968, 824553, 8495560, 102689741, 1317098772, 18729163609, 270642677396, 4396374315075, 73997950572016, 1318896555293137, 24900891903482832, 499312682762581945, 10301544926241347140, 227464062944112566481
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^x))
-
a087906(n) = (n-1)!*sumdiv(n, d, 1/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a087906(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
A356596
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^(1/k!) )^exp(x).
Original entry on oeis.org
1, 1, 5, 25, 162, 1231, 10988, 109481, 1220005, 14915924, 198841997, 2861122716, 44290863499, 731732469209, 12865489418525, 239613961313353, 4712991199268122, 97557259778360215, 2120682504988009054, 48270952330701285107, 1148400573894718809487
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^exp(x)))
-
a354338(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!))/(n-k)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354338(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-6 of 6 results.