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 A362897 Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of endofunctions on an n-set with k endofunctions. 3
 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 7, 1, 1, 1, 13, 74, 19, 1, 1, 1, 22, 638, 1474, 47, 1, 1, 1, 34, 4663, 118949, 41876, 130, 1, 1, 1, 50, 28529, 7643021, 42483668, 1540696, 343, 1, 1, 1, 70, 151600, 396979499, 33179970333, 23524514635, 68343112, 951, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Isomorphism is up to permutations of the elements of the n-set. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals). FORMULA T(0,k) = T(1,k) = 1. EXAMPLE Array begins: ====================================================================== n/k| 0 1 2 3 4 5 ... ---+------------------------------------------------------------------ 0 | 1 1 1 1 1 1 ... 1 | 1 1 1 1 1 1 ... 2 | 1 3 7 13 22 34 ... 3 | 1 7 74 638 4663 28529 ... 4 | 1 19 1474 118949 7643021 396979499 ... 5 | 1 47 41876 42483668 33179970333 20762461502595 ... 6 | 1 130 1540696 23524514635 274252613077267 2559276179593762172 ... ... PROG (PARI) permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} K(v, m) = {prod(i=1, #v, my(g=gcd(v[i], m), e=v[i]/g); sum(j=1, #v, my(t=v[j]); if(e%(t/gcd(t, m))==0, t))^g)} T(n, k) = {if(n==0, 1, my(s=0); forpart(q=n, s+=permcount(q) * polcoef(exp(sum(m=1, k, K(q, m)*x^m/m, O(x*x^k))), k)); s/n!)} CROSSREFS Columns k=0..3 are A000012, A001372, A054745, A362898. Row n=2 is A002623. Main diagonal is A277839. Cf. A362644. Sequence in context: A081297 A110180 A328718 * A005765 A360289 A343717 Adjacent sequences: A362894 A362895 A362896 * A362898 A362899 A362900 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, May 10 2023 STATUS approved

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Last modified February 22 21:30 EST 2024. Contains 370265 sequences. (Running on oeis4.)