Original entry on oeis.org
1, 1, 5, 70, 1973, 94216, 6851197, 706335064, 98105431657, 17669939141440, 4006704580744601, 1117139031649249984, 375701872315954792093, 149988716080978525265776, 70129434038848683974552365
Offset: 0
-
{a(n,k=0)=local(F=x, xEx=x*exp(x+x*O(x^(n+k+1))), M, N, P, m=n+k); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, xEx)); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); n!*(P~*N~^-1)[n+k+1, k+1]}
Original entry on oeis.org
1, 2, 16, 308, 11048, 639972, 54671188, 6471586298, 1014487323984, 203492881479464, 50842872702666524, 15484223252089602342, 5646860009850046968472, 2429577079632942917710580
Offset: 0
-
{a(n,k=1)=local(F=x, xEx=x*exp(x+x*O(x^(n+k+1))), M, N, P, m=n+k); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, xEx)); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); n!*(P~*N~^-1)[n+k+1, k+1]}
Original entry on oeis.org
1, 3, 33, 810, 35325, 2408568, 236624733, 31654735416, 5532363865977, 1223887080470256, 334272773792556369, 110467177430468340408, 43442224822360939240629, 20048090531903711663566248
Offset: 0
-
{a(n,k=2)=local(F=x, xEx=x*exp(x+x*O(x^(n+k+1))), M, N, P, m=n+k); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, xEx)); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); n!*(P~*N~^-1)[n+k+1, k+1]}
Original entry on oeis.org
1, 4, 56, 1672, 85904, 6741544, 749040472, 111786940612, 21558649749088, 5215883627856592, 1546429233541304456, 551278120123210461436, 232603216443181020788944, 114634034948809175011787176
Offset: 0
-
{a(n,k=3)=local(F=x, xEx=x*exp(x+x*O(x^(n+k+1))), M, N, P, m=n+k); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, xEx)); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); n!*(P~*N~^-1)[n+k+1, k+1]}
A174480
Rectangular array of coefficients in successive iterations of x*exp(x), as read by antidiagonals.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 15, 23, 1, 1, 5, 28, 102, 104, 1, 1, 6, 45, 274, 861, 537, 1, 1, 7, 66, 575, 3400, 8598, 3100, 1, 1, 8, 91, 1041, 9425, 50734, 98547, 19693, 1, 1, 9, 120, 1708, 21216, 187455, 880312, 1270160, 136064, 1, 1, 10, 153, 2612, 41629
Offset: 1
Form an array of coefficients in the iterations of x*exp(x), which begin:
n=1: [1, 1, 1/2!, 1/3!, 1/4!, 1/5!, 1/6!, ...];
n=2: [1, 2, 6/2!, 23/3!, 104/4!, 537/5!, 3100/6!, ...];
n=3: [1, 3, 15/2!, 102/3!, 861/4!, 8598/5!, 98547/6!, ...];
n=4: [1, 4, 28/2!, 274/3!, 3400/4!, 50734/5!, 880312/6!, ...];
n=5: [1, 5, 45/2!, 575/3!, 9425/4!, 187455/5!, 4367245/6!, ...];
n=6: [1, 6, 66/2!, 1041/3!, 21216/4!, 527631/5!, 15441636/6!, ...];
n=7: [1, 7, 91/2!, 1708/3!, 41629/4!, 1242892/5!, 43806175/6!, ...];
n=8: [1, 8, 120/2!, 2612/3!, 74096/4!, 2582028/5!, 106459312/6!, ...];
n=9: [1, 9, 153/2!, 3789/3!, 122625/4!, 4885389/5!, 230689017/6!, ...];
n=10:[1, 10, 190/2!, 5275/3!, 191800/4!, 8599285/5!, 457584940/6!,...];
...
This array begins with the above unreduced numerators for n >= 1, k >= 1.
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{T(n, k)=local(F=x, xEx=x*exp(x+x*O(x^(k+1)))); for(i=1,n,F=subst(F, x, xEx));(k-1)!*polcoeff(F, k)}
Showing 1-5 of 5 results.
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