We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as the blockength tends to infinity, and the limit is obtained via density evolution. The finite-blocklength correction behaves like alpha(epsilon, t)/n + Theta (n(-2)) as the blocklength tends to infinity where alpha(epsilon, t) denotes a specific constant determined by the code ensemble considered, the number of iterations, and the erasure probability of the BEC. In this paper, we derive a set of recursive formulas which allows the evaluation of the constant alpha(epsilon, t) for standard irregular ensembles. The dominant difference alpha(epsilon, t)/n can be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using alpha(epsilon, t) is accurate even for small blocklengths.